ISBN - 978-605-5631-57-4 Sertifika No: 11748
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ISBN - 978-605-5631-57-4 Sertifika No: 11748
ISBN - 978-605-5631-57-4 Sertifika No: 11748 GENEL KOORDİNATÖR: REMZİ ŞAHİN AKSANKUR REDAKTE: REMZİ ŞAHİN AKSANKUR SERDAR DEMİRCİ SABRİ ŞENTÜRK SERVET SAVAŞ ÇETİN %DVÜP<HUL(926%$6,0$1.$5$ %XNLWDEÜQWÖPEDVÜPYH\D\ÜQKDNODUÜkartezyen eg QDDLWROXS WÖPKDNODUÜVDNOÜGÜU.ÜVPHQGHROVDDOÜQWÜ\DSÜODPD]0HWLQYHVRUXODU NLWDEÜ\D\ÜQOD\DQíLUNHWLQÐQFHGHQL]QLROPDNVÜ]ÜQHOHNWURQLNPHNDQLN IRWRNRSLWDUDPD\DGDKHUKDQJLELUND\ÜWVLVWHPL\OHÁRðDOWÜODPD] \D\ÜQODQDPD] 7XUJXWUHLV0DK*L\LPNHQW6LWHVL(%ORN%$1R(6(1/(5ñ67$1%8/ 7HO)D[ www.kartezyen.com.tr Copyright © kartezyen eg 75ñ*2120(75ñ Dar Açıların Trigonometrik Oranları: B!.;C!4;C &#!.! & 'D .! -## # ! &.- &!)/& !) ' A hipotenüs D= Karþý dik kenar +#D= B a C D= Komþu dik kenar +#D= 0 -## & !E F.-1* )& (!/ D G$#(!/ #)& (!/ G$#(!/ )& (!/ #)& (!/ #)& (!/ )& (!/ I EI I I +# D IEI I I D I EI IEI +# D IEI I EI çözüm kavrama sorusu A A Hipotenüs Karþý dik kenar 3 5 3 5 4 B C 4 B Komþu dik kenar C E.--* % )& (!/ :E== G$#(!/ E.-%JKAJEK%IIL2 %IEIL> %IEIL6 #!&/-* % sin(A n I I :E= I EI :E= 2 6 Cevap: çözüm kavrama sorusu A A 3 Komþu ñ5 dik kenar ñ5 B 3 5 2 B C Hipotenüs C 2 Karþý dik kenar E.-%JKAJEK%IIL6 %IEIL< < < < IEI LII MIEI #!&/-* % cos(B < < < < IEI L:6= M< < IEI L6M>IEI L4IEIL2 +#:E== #)& (!/ G$#(!/ I I 6 I EI 2 Cevap: 2 5 3 Trigonometri - 1 soru 1 soru 5 A JKAJEK JKAJEK 13 5 IIL6 A ñ6 ñ3 IIL2 IEIL3< IEIL? IEIL32 B #!&/-* % #!&/-* % C 12 tan(A B C sin(B 6 = 32 soru 2 3< = 32 6 E= 3< P D= 3< = 3 32 = 3< soru 6 A JKAJEK 3 ñ2 IIL< = < E= 2 D= 3 < = 3 2 A 1 IEILP B IEIL2 B C ñ7 #!&/-* % sin(A C 3 JKAJEK%IIL3 %IEIL2 #!&/-* soru 3 2 P = E= < P D= P 2 = < 2 A JEKAJEK IEIL2 4 IEILP 3 0NO808YAYINLARI cot(A P < = = 3 2 = 2 soru 7 E= < < 2 D= 3 < < = < < A 1 IIL> B #!&/-* % B cos(B C ñ7 C ò15 JKAJEK%IIL3 %IEIL36 #!&/-* % sin(ACB)+cos(B = 2 > soru 4 = P > E= 2 P D= > P = P 2 = ò10 JEKAJEK IIL3; B = 3 3; E= D= 3 2 3–A > 36 = 3 36 > C ñ2 A B ñ3 = 2 < 6 36 = D= 2–E D= tan(BCA)+cos(ACB) 2 3; 3 36 #!&/-* % = 1–B E= IEIL< #!&/-* % cos(A = 3 3 < IIL2 C 3 = JKAJEK 1 IEIL3 IEIL2 soru 8 A 3 > 4–C 5–B 3 < 36 3; 6–E 2 6 36 E= = 3 3; 3; 2 36 3; 7–E 8–D Trigonometri - 1 çözüm kavrama sorusu D a D&* -. &%D..&!&/ &. -#!) .!)!' C k D F 3k a C IIL&!% IIL2II #!&/& A E B 2k 2k 2k IIL2& ' IDEILIIMII ED&&* -%:DE=LDIIL2IIIDEIL<IDI A #!&/-* % sinD+cosD E k B 3k LM2 L> IDEIL<IDI#!&/&IDILI@IL<& ' F < 3k a < IEI LI@EI MI@I C < < < L:2= M:<= < < L4 M> 2k ò13k < L32 IEIL32 E < < ²¦¦ ¦ < 2 32 32 ¦¦ » B +# B 2 2 ¦¦ 32 32 +# B ¦¦ 32 32 ¦¼ B 6 32 Cevap: 5 13 çözüm kavrama sorusu 1 a 1 1 1 1 1 1 1 a 1 &)!*(&) ! &#!) !) ' a D . .& !&/ &.- ! ! # (' (& D . ! !&/( . -).!) (' 1 1 1 D 1 1 a a 1 4 4 br 1 1 1 B > < & ' < a 2 br Cevap: 2 Trigonometri - 1 soru 1 A soru 5 D a ED&&* -% *(&) ! & E IDIL<II :D=LD #!)) ' D C B #!&/-* % = sinD 3 3P soru 2 < 3P = E= 2 3P > 3P D= = soru 6 D ED&&* -% B = 2 < E= 3 D= D 3 < = 3 2 C a ED % :ED=LD 0NO808YAYINLARI = 2 6 = > 6 = > 2 a E= 2 6 D= 2 > &)! *(&) ! & sinDD A = < < soru 7 6 2 = sinD.cosD 3 > 6 #!)) ' #!&/-* % 3 < E= D= 3 > = = 2 < A a B 3 < 3 6 soru 8 D a ED % < 6 = E= #!)) ' #!&/-* % cosD+cotD tanD+ cotD B 2–B E 32 D= 6 3–C > 6 = P 6 &)! :=LD 3P E= 36 D= a *(&) ! & << = 36 2 6 IEIL>IEI 1–A D= D #!&/-* % tanD 2< = 36 < 6 #!)) ' C :ED=LD soru 4 E= *(&) ! & a IEIL2IDEI = 3 6 = &)! IILIDI soru 3 3 > 3 > E A = < a &)! IIL<II = C = 4 = 6 4–A 6 < 5–C 5 = 32 ? E= 6–E 33 ? D= 7–A 2 < = 3 ? 8–B Trigonometri - 1 D& .#!( QD%+#D%D%+#D# ! & - !$&/ ! # !&/& &.-.(!$ ! # ! &.-( !) ! &/ -## # ! ! ' çözüm kavrama sorusu ;CRDR4;C#!( % D& .#!&/& &.-.(!$ !# ! 2 B 6 #!&/-* % cosD !) ! ' )& (!/ D= G$#(!/ 2 6 A < < < < < II LIEI MIEI 5 < 6 LIEI M2 3 IEIL> a 4 B +#D= C #)& (!/ G$#(!/ > 6 4 5 Cevap: çözüm kavrama sorusu D& .#!&/& &.-.(!$ !# ! !) ! ' )& (!/ 6 D= 3< #)& (!/ A ;CRDR4;C#!( % 6 B 3< #!&/-* % cosDD 13 a B < < 5 C 12 < II LIEI MIEI < < < II L6 M3< +# B 3< 6 B ! ' 32 32 +# B B ;CRDR4;C#!( % +#D= +#D=2 2 3< 6 P 32 32 32 Cevap: 7 13 çözüm kavrama sorusu IIL32 #)& (!/ )& (!/ 2 3 A 2 #!&/-* % sin D D < 2 < < II LIEI MIEI 1 < < < II L3 M:2= IIL< a B ñ3 B 3 2 +# B < < C < 3¬< 2 ¬ 3 2 < 3 < B +#< B < ® < ® > > < > Cevap: 6 1 2 Trigonometri - 1 soru 1 soru 5 ;CRDR4;C#!( % ;CRDR4;C#!( % 3 < #!&/-* % cosD B 2 < = soru 2 = 3 < +#DL2 #!&/-* % sinD E= 3 2 3 > D= = < < = 3 2 soru 6 3 < = E= ;CRDR4;C#!( % 3 +# B > #!&/-* % sinD soru 3 = < < < 3; > E= D= 32 > = 36 > = 3 6 soru 7 = < 6 E= ;CRDR4;C#!( % soru 4 = <6 <> < 6 D= 3 6 = 6 < 3 < = 2 < P B <6 #!&/-* % tanD <> <6 2 3; DL< ;CRDR4;C#!( % = = #!&/-* % sinD.cosD 0NO808YAYINLARI 3 > 3 3; D= ;CRDR4;C#!( % = 3 < < +#DL3 2 2 #!&/-* % tan D D E= <> P D= P <> P <6 = = 3 < soru 8 = 3 2 E= 3 2 D= ;CRDR4;C#!( % ;CRDR4;C#!( % 3 B < #!&/-* % cotD > 6 2 2 2 #!&/-* % sin D D.cos D = 1–A 3 2 = 2 < 2–E +# B E= 3 < D= < 3–D = < 2 =S< 4–D 5–D 7 =S3 E=; 6–B D=3 7–A =< 8–C Trigonometri - 1 çözüm kavrama sorusu A A a b 10 10 a a H B b H C 3k I GI I GI 2 º º I GI ? G.-&% B I I 3; 6 C B E.-%JKAJEK%JGKAJEK%IIL3; %:E=LD B 5k 6 2 #!&/-* % 6 GE.-&% B IGEI 2 #!&/&% I EI 6 IGEIL2IEIL6&!' < < IEI LIGI MIGEI < < < < < < < :6= L? M:2= <6 S4 L2? 3? L2? 2 < 2 36 15 IEIL6#!&/&% I EI 6' Cevap: < < 2 çözüm kavrama sorusu A A 2 2 a B a B C D 2ñ3 ñ3k D k C H 3 E.-%:DE=LDIILIEI%IDIL< %IEIL? 3 &DE.-&%D=2#!&/-* % JGKAJEK#!+)!&JGKT.(!' DG.-&% I GI B 2 º I GI IDGI < < < 2 % IDGI &!' < < IDI LIGI MIDGI < L:2= M < < >L> L3 IGIL2 IDGIL3 GE.-&% < < < < < < IEI LIGI MIGEI IEI L:2= M2 < < IEI L2M4IEI L3< IEIL<2 çözüm kavrama sorusu A Cevap: <2 D 8 8 A E E 4 D b 4 a B a b C B DaDE%D.-&% +# B ED&&* -%JDKAJEK%IDIL5 %IIL> :ED=LD#!&/-* %cotD! a C I DI 5 < I I > Cevap: 2 8 Trigonometri - 1 soru 1 soru 5 A a &E.-& E) .-% JKAJEK IIL3< JEKAJGK :D=LD :G=LD B A H 1 C 12 a IGEIL3 #!&/-* % 3 B #!&/-* % < " = 2 < = soru 2 < 2 E= 3 < < < D= < 2 = =3 a &E.-& JKAJEK :DE=LD IIL2 H C soru 3 E=> D=6 =? A &E.-& soru 7 :G=LD IIL2 B C H soru 4 =<32 E=<36 D=236 = =23; < 2 2 2 2 D= = D a 3 E B = > 6 E= C 4 < 2 D= 3 < = A D E JKAJDK 2ñ5 2 :=LD IILIEI IDEIL< a B IEIL<6 D DL<#!&/-* % C DL3#!&/-* % =? 2–E E=P D=5 3–B 2 < a ED&&* - IEIL>IDI < 6 6 A 2 6 soru 8 :DE=LD 1–B E= sinD! E.- => 3 2 #!&/-* % C A = IEIL> b a 2 %IEIL? #!&/-* % < =32 C ED&&* - JDKAJEK DL2 a E < 2 = JGKAJEK :EG=LE D #!&/-* %cosD! 0NO808YAYINLARI =2 =? B IIL3 2 #!&/-* % < =< D=> 1 3 :GE=LD +# B E=2 ED&&* - JKAJDK B C A JEKAJGK IEIL>2 B =< soru 6 A D DL<2 =3 =3; 4–D 5–C 9 B =2 E=> 6–B C D=6 7–A =? 8–A Trigonometri - 1 30°– 45° ve 60° lik açıların trigonometrik oranları 2;C%>6C?;C!.! -## # ! !.2;S?;S4;>6S>6S4;:( &.-=*(!.-! & ,&!! ('0 -## #. &.# )(.# ! 2;C%>6C?;C!# ! & ' 2;S?;S4;.- >6S>6S4;.- A A 60° 2 br B 30° 45° ñ2 br 1 br 45° ñ3 br C B &.- &!% 2;n 3 < ?;n 2 < 3 < +# 2;n 2 < +# ?;n 2;n 3 2 ?;n 2 +# 2;n 2 +# ?;n 3 2 3 < >6n >6n 3 C +# >6n 3 < +# >6n 3 çözüm 2;C'+#2;C 2;n 2 3 +# 2;n #!&/&% < < 2;n'+# 2;n 3 2 2 ' < < > Cevap: 3 4 çözüm kavrama sorusu 1 br &.- &!% kavrama sorusu 1 br ?;C'2;CS+#2;C'+#?;C ?;n # +# 2;n 2 3 % 2;n < 2 2 3 % +# ?;n #!&/& < 2 ?;C'2;CS+#2;C'+#?;CL 2 3 2 3 ' ' ; < < 2 2 Cevap: 0 çözüm kavrama sorusu >6n'+# >6n >6n +# >6n # 3 3 % +# >6n < < >6CL3%+#>6CL3#!&/& 3 3 3 ' >6n'+# >6n 3 3 3 1 < < < ' Cevap: >6n +# >6n 3 3 < < < > 4 >6n 10 Trigonometri - 1 soru 1 soru 5 2 2 <'2;C 3 < = 3 E= 2 D= 2 < = < = soru 2 soru 3 = 2 < E= 3 D= 3 < = 3 2 >6CM+#>6C soru 4 3 < = 1–B = < E= < D= 2 < E= 3 D= 3 2 3 < = 2 soru 8 2–D < < = >6C'>6CM+#>6C'+#>6C = = < =2 2 < ?;n +# ?;n =? D= ?;C'+#2;C soru 7 < < E= ; = 2 = < 2 < = 0NO808YAYINLARI 2 3 2 < soru 6 +# 2;n 2 = 2;n = = < E= 3 D= 3 < = 2 < >6n +# >6n +# >6n >6n E=3 D=< 3–C =2 =2S<< 4–E 5–C 11 =3S<< 6–A E=<S3 D=2 7–B =< 8–A Trigonometri - 1 4;C!.$& '0! .! & &/ #)!& U&/ #U) ' A a c D+EL4;C:0! .! = a a B % +# C DL+#E& ' + + b B a a % +# C DL+#E& ' b B a C çözüm kavrama sorusu 26CS+#66C 26CM66CL4;C#!&/&! .! & ' # 26CL+#66C 26CS+#66CL+#66CS+#66CL; Cevap: 0 çözüm kavrama sorusu P;CM<;CL4;C>;CM6;CL4;C#!&/&%P;C!<;C P;n +# <;n 3 >;n' +# 6;n # >;C!6;C! .! & ' P;CL+#<;C>;CL+#6;C P;n +# <;n +# <;n +# <;n ; ; 3 3 3 >;n' +# 6;n ' +# 6;n +# 6;n Cevap: 0 çözüm kavrama sorusu >2CL+#D >2CL+#D>2CMDL4;CDL>PC <PCL+#E <PCL+#E<PCMEL4;CEL?2C D+EL>PCM?2CL33;C #!&/-* %D+E Cevap: 110° çözüm kavrama sorusu D+EL4;C#!&/&! .! & ' A DL+#E& ' a < < < < !&% DS+# EL ES+# EL;& ' Cevap: 0 b B C E.-%JEKAJEK%:E=LE:E=LD 2 2 #!&/-* %sin D E 12 Trigonometri - 1 soru 1 soru 5 %&'#!*# =+#<PC =<PC E=+#?2C D=?2C =+#?2C DL+#P3C EL+#<<C #!&/ -* % D+E #! * =PPC soru 2 soru 6 ,,'#!*# =>>C =+#6?C E=+#>;C D=6?C =>?C =P5C 3;CL+#5;CL6S5#!&/-* % =3 =< E=2 D=> =6 DL+#22C :DM3;=L+#:ES<;= soru 7 =P;C ED&&* - =3;;C C b :DE=LE #!&/-* % =S< soru 8 >2n' 6?n +# 2>n'+# >Pn a D=4;C :D=LD E A E=5;C D sinDE soru 4 =55C #!&/ -* % D+E #! * 0NO808YAYINLARI D=5PC =P6C soru 3 E=5>C =S3 E=; D B D=3 =< C b ED :DE=LD :DE=LE 3 = > 3 = < E= 3 D= < #!&/-* % = > B +# B +# C C # = < 1–C 2–E 3–B 4–C 5–D 13 = 3 a A E= 6–E 3 < B D= 7–C 3 > = 3 5 8–A Trigonometri - 1 )!-.#! #!) !)& ' B Açýnýn dýþ bölgesi JJ)! . ! & ' Açýnýn iç bölgesi Açýnýn köþesi O & ! . *) # # & #!+ )!& B.&-* ! ' A Açýnýn dýþ bölgesi . & )!-. &/ & ' G- )!-. - #!&/ . * /!& '* *&.! :M=$#(,*!%*&.! -,*!& ' B rý ena im k Bit a Baþla O ngýç gýç aþlan B kena AOB açýsý (+) Pozitif yönlü açý rý O rý kena B BOA açýsý () Negatif yönlü açý a Bitim kena rý A A . *!.% := .& -* ! ' . *!. ! & # ! .& +!+ ' & $#(,*!.*!.:=LD-,*!.*!.:=LSD& ' çözüm kavrama sorusu A Bitim B A ý r kena B Pozitif yön Baþla ngýç C &E.$#(,*! .#!&/-* %#/0113 kena rý C JE)!-. % J & ' çözüm kavrama sorusu ED.-,*! .#!&/-* %#/0113 gýç aþlan B rý kena C Negatif yön D Bitim JDE)!-. % JD & ' 14 kena rý E Trigonometri - 1 soru 1 soru 3 D #565610$ #!* O a A) B) O O E 4/*#!*- A B B A B A gisi 0# C) = )!-. J)& ' D) = JD)& ' A O E= X#(,*! .& ' D= -,*! .& ' B O = :D=LD& ' soru 2 #!/*10$ A) B) A 0NO808YAYINLARI E) O B A soru 4 70$6#!* A) O B) C C B O B C) C D K M O D) F B C) D) B C C B O E O O E) O E) L O B O O C M 1–D 2–C 3–E 15 4–B Trigonometri - 1 Birim Çember: D## &( & (# U#! .$3 #!. & '0 -## ,##! . &!!+ ' < < < (:%= .$ #!. &!:AS= M:S= L & ' . (:;%;= .$3 #!&/&% < < < :AS;= M:S;= L3 A M L3 < < . &!& ' . *!-! )/&-& ' y y 1 x2+y2=1 1 1 2.bolge x 1 1.bolge 1 1 1 3.bolge 1 x 4.bolge çözüm kavrama sorusu 2 ¬ X % # . ( &#!&/-* % < ® 2 ¬ X % # . ( &#!&/& < ® 0!!13 A M L3 . &!/! ' < < 2 ¬< 2 3 < < < 3 3 > > ® 3 < 3 & ' < Cevap: y 1 2 3 ¬ # . ( &% X A% < ® 1 1 1 A < < 3 3 ¬< 3 3 3 A < 3 A < < ® < < x 3 3 A < < X# . &<'*!-&#!&/&% 1 4$1/#813 A A 3 & ' < Cevap: 1 2 çözüm kavrama sorusu 3 X % < veya çözüm kavrama sorusu P x, 1 ñ2 1 2 ¬ # . ( &>'*!-& ® y A < < 3 3¬< < 3 < ® #!&/-* %0 x P 1 ,y 2 16 < 2 2 º & ' > < Cevap: 3 2 Trigonometri - 1 soru 1 3 X % > soru 5 ¬ # . ( &#!&/-* % ® y P x, ò10 4 4 $1/# 01! x 8 = 3 > = 2 > E= 2 > D= 3; > 36 > = = soru 2 3 5 = soru 6 3 ¬ X % # . ( &#!&/-* % < ® 2 5 E= 6 5 2 > D= ? > = y P x, 1 3 4 $1/# 0! x 8 = 3 > = 3 < E= 3 < D= 2 < 6 < = soru 3 6 ¬ X A% # . ( &'*!-&#!&/ 2 ® -* %9 0NO808YAYINLARI = 6 2 = D= soru 7 ? 2 < < 2 E= < 2 2 3; 2 = y 4 $1/# x 8 = < 2 = < 2 E= 3 2 D= 3 2 = < 2 P ñ3 , y 2 = soru 4 3 < soru 8 = 2 < = 3 < y x 8 P 1 ,y ñ5 = 3 6 = D= 3–A < < D= $1/# 3 3 3 5¬ 3¬ 3 ¬ = % = % E= % < <® 2 2® < ® < 3 ¬ ¬ 2 2 32 D= % = % < ® > ® < > 2–C 3 < < 4 X:A% = # . ( & ' *!-& #!&/ -* %#!* 1–E E= 4–E 5–E 17 3 6 E= 6 6 = 6–D 7–A 2 6 < 6 6 8–E Trigonometri - 1 Açı Ölçü Birimleri: .! *!..!!&/( ! & + && '0. 2?;)$ .*!&/&$ .! & -* (.*!.3& +& 3C.&-* ! '0. 2?;C& 'G - . *!.:=!-* ! ' Y .$)(!. -* (.*!.3 &!.& ' . & L3 #!&/&. . <S'3L<S& '3 !(!/&<S & '&&#!. <S && ' A 1° lik açý O A Çember yayýnýn 1 360 B O 0. 2?;C 1 radyanlýk açý 1 br 1 br uzunluðundaki yay B 0. <S && ' 0. & +#! 2?;& +% &#! <S &)#!&/&.*!. &% D &!) ! $!&/&% 2?; <Q D:& += : &= 35; Q # !&&! ' çözüm kavrama sorusu :;0$$! D /&% 35; Q 2; 35;'L2;'S 35; Q 2;Q 35; Q && ' ? Cevap: Q 6 çözüm kavrama sorusu :=L<>;C#!&/-* %$$0 D /&% 35; Q <>; 35;'L<>;'S 35; Q <>;Q 35; >Q && ' 2 Cevap: 4Q 3 çözüm kavrama sorusu 11Q 0$$ 6 33Q 33'35; 33'2; 22; ? ? D #!&/&35;C!.S &!. 35;n Q *!.) '(& &#! !. ! &S 35;& +(! (' 18 Cevap: 330° Trigonometri - 1 soru 1 soru 5 Q 0$$$$#!4 * ,>$$0$$#!* = Q ? soru 2 = Q > E= Q 2 D= Q < = <Q 2 =36C soru 6 2Q 6 <Q 2 E= 6Q ? D= >Q 2 = 2Q < 6Q ? soru 4 = PQ ? E= 6Q > D= PQ > = 33Q ? 1–B soru 7 soru 8 = 6Q < 2–C E= 3>Q 2 D= 2Q 3–B = =3;6C =P6C E=3<;C D=326C =36;C =36;C =<3;C E=<>;C D=<P;C =2;;C 7Q 0 $$ $$ #!2 * >,;' $$ 0 $$ #! * = <Q D=?;C 5Q 0 $$ $$ #!3 * %@;' $$ 0 $$ #! * = E=>6C =P6C 0NO808YAYINLARI soru 3 = =2;C 5Q 0 $$ $$ #!12 * @>;' $$ 0 $$ #! * = PQ < =2P6C 4–D 5–C 19 =24;C E=>6;C 6–A D=6>;C 7–E =?2;C 8–E Trigonometri - 1 0 -## #. &*!.& + &#! !.! .#/!!.. ( &-* +/(' y O y P 0° ve 0 radyan P x O y 90° ve p radyan 2 x A y O P 180° ve p radyan A y A x P x O 270° ve A P O 3p radyan 2 x 360° ve 2p radyan XX.*!. X.*!. X.*!. X.*!. X.*!. ;C; && ' Q 4;C && ' < 35;CS && ' 2Q <P;C && ' < 2?;C<S && ' çözüm kavrama sorusu 4 y $1/# D /&% 35; Q >6 Q >6 35;'L>6'S 35; 35; Q P 68$$ 0 45° A O x Q && ' > Cevap: Q 4 çözüm kavrama sorusu y Bitim kenarý P 30° P Baþlangýç noktasý 90° 30° x O y x O Baþlangýç kenarý # X #! . & + #! *!. !& 4;M2;L3<;& ' 400$18 0$$ D /&% 35; Q 3<; Q <Q 3<; 2 35; 35; Q . ( &# !. ! )!-.#! :3%;=#& ' Cevap: 2Q 3 çözüm kavrama sorusu y y p p+ 6 p 6 O x O Bitim kenarý P P Baþlangýç noktasý x Baþlangýç kenarý #X#!.*!. &#! !& 400$18 $$$13 Q Q PQ & ' ? ? P'35; PQ &!.L LP'2;L<3;C& 'Cevap: 210° ? ? 20 Trigonometri - 1 soru 1 soru 5 y 4 y P 4 15° $1 $1 P x O O 8 8 $$0 $$ = Q 2; soru 2 = Q 36 E= Q 3< D= Q 3; = Q 4 =36C soru 6 y 4 =2;C E=>6C P 30° x O P $$ soru 3 6Q 2 E= 6Q > D= <Q 2 = 2Q > y 4 0NO808YAYINLARI 8 = $1 = <Q 2 E= D= 6Q 2 = 6Q > soru 8 =34;C O x P E=<;;C D=<3;C =<>;C y $1 O x 30° 8 $$0 1–C p 6 4 $1 6Q ? 4 =356C y =3>6C y $$ 2Q > D=326C 8 4 = E=3;6C P $$0 soru 4 x 45° 8 Q > soru 7 =P6C $1 O = =>6C x O $$0 6Q ? p 4 8 = =P;C y $1 x D=?;C 4 $1 p 4 = 6Q 2 2–A 8 $$ P E= >Q 2 D= 3–E <Q 2 O = 2Q > =<5;C 4–B 5–C 21 =2;;C E=23;C 6–D x p 6 D=2<;C 7–D P =22;C 8–E Trigonometri - 1 X#(,*!.! &#!&/--,*!.! & . ( &-* ! (' y y Bitim kenarý P Baþlangýç kenarý a x O O x a Baþlangýç kenarý Bitim kenarý P çözüm kavrama sorusu &;0$113 y 90° 180° 0° O x 70° P 270° çözüm kavrama sorusu y y Pozitif yönlü 90° 40° O 180°+40°=220° derece 180° x 40° P 0° O x P 270° y 4 $1 8 /#10$/0$ $13 90°( 270°) (180°) 180° 40° O 0° x Negatif yönlü (180° 40°)=140° P 270° ( 90°) Cevap: 220°, – 140° çözüm kavrama sorusu p y 2 y P p 4 O p x P p 4 O 2Q Q 6Q < > > 22 3p 4 0 x O p P 3p 2 X#(,*!% 4 $1 8 /#10$/0$0 $13 Pozitif yönlü 3p p = 5p 2 4 4 p 4 y x Negatif yönlü p p 3p p 4 + 2 = 4 2 -,*!% Q Q¬ 2Q 6Q 2Q Cevap: % > < ® > > > Trigonometri - 1 soru 1 soru 5 y 4 8 x =S36;C E=S<>;C D=S2;;C =S22;C = PQ ? soru 6 y P 4 = x O p 3 D=S<>;C =S2;;C y = <Q 6 = D= soru 7 6Q ? $1 x 81 0$$$ E= 6Q 2 soru 4 =2;;C E=<5;C D=<P;C P =<>;C = 2Q > soru 8 y = 6Q > E= $1 $1 P 0$$$ x D= = 33Q > P O 81 165° 4Q > y 4 O PQ > 4 81 x p 4 O 0$$$0 P =2<;C 2Q > y $1 60° <Q 2 4 O P = 4 81 x O 0$$$0 0NO808YAYINLARI soru 3 34Q 3< 32Q 3< y 8 0$$$ E=S3<;C E= = $1 120° 8 =S?;C 3PQ 3< 33Q ? 4 $1 =S2;C x 0$$$0 D= soru 2 O 8 0$$$ =S?;C p 12 $1 30° O P 4 P $1 y x 7p 6 0$$$0 =346C 1–E =<;6C 2–D E=<36C D=<<6C 3–B = =<26C 4–A 6Q ? 5–E 23 = 6Q 2 E= 6–B >Q 2 D= 7–C 2Q > = <Q 2 8–A Trigonometri - 1 Esas Ölçüsü: .*!.2?;& +<S &) 'B!.2?;C&<S &&#!.! )!-.# & -. ! ' y y y P a O P P a x a x O O 360°+a açýsý x 720°+a açýsý &)!! &-* !&/-%D.2?;C! !&/&##!& ' ;GDR2?;C#!( %D.:DM2?;C=%:DMP<;C=%:DM3;5;C=%'''.! *!.& 'N#!( DM'2?;C!.*!.D& +& ' ;GDR<S#!( %DM'<S:N=.! *!.D && ' çözüm kavrama sorusu >H;' / @,;;' $$ 13 . ( & )!-. #& )!$ 2?;C ! $ # <<;C & ! ! X x #-! '*! .<<;C& ' y 220° Z! .( *!. ! 65; #&:2?;=-* &/ !& #!& '. 2?;T*!&!*!.& ' O P 3>;;C!.*!.% 580 360 360 1 Esas ölçü 220 1400 360 1080 3 Esas ölçü 320 Cevap: 220°, 320° çözüm kavrama sorusu &#! !).! *!.! !.. .&!<S! ! ' 33Q 22Q 0/ 0 4 3 $013 11S0 33Q 3;Q N Q Q *!.& ' <S #!&/. ! &! ' 22Q 2<Q Q 2<Q Q > > > > º 5Q Q Q *!.& ' > > <<Q <3Q Q <3Q Q 2 2 2 2 PQ Q Q >Q *!.& ' ?Q Q 2 2 2 Cevap: Q% 24 Q >Q % > 2 Trigonometri - 1 soru 1 soru 5 ,&;$$ =4;C soru 2 =3;;C E=33;C D=3<;C 7S0$$0 =32;C = J:;'$$ =3;;C E=3<;C D=32;C =<P;C soru 4 E=2;C D=>;C =6;C 1–C soru 7 = =<3;C 2–E E=<<;C D=<>;C 3–B = = <Q Q < E= Q 2Q < D= = <Q 2Q < soru 8 = Q < E= Q > D= 2Q > = 6Q > = 6Q ? <6Q 0$$0 ? @:%;'$$ =<;;C 2Q < D= 32Q 0$$0 > @@;;'$$ =<;C E= Q = ; =3;C Q < = 18S0$$0 0NO808YAYINLARI soru 3 Q 2 soru 6 =4;C =<?;C = 4–D Q 2 5–C 25 = Q ? E= 6–A <Q 2 D= 7–E Q < 8–B Trigonometri - 1 -,*!.! *!..J;%2?;C=J;%<S= & &!$#(,*!& ' çözüm kavrama sorusu ,;;'$$$13 -,*&>;;C! y !&/& # )!&-X#! ' *!. J;% 2?;= 320° O x 40° !/& #! - /& . $# (,*! )!/#! P 2<;C*!.& ' Cevap: 320° çözüm kavrama sorusu 1. Yöntem: @&;'/H;;'$13 S3P;C2?;C SS2?;CS3 *!. 34;C Z!.(&*!.! !.* & ' Birincisi;2?;*! !! '+*!& &(- !$#(,.- /& ' S5;;C2?;C SS3;5;CS2 *!. <5;C 2. Yöntem: OP .! $#(,*!#! &)$!# .! 2?;&. ' 3P;R2?;C#!&/&*!- !& 2?;S3P;L34;*!.! ' S5;;C!.5;;C:$#(,*!-=&)! % 5;;C2?;C SP<;C< 5;C !#.2?;&. ! ' 2?;CS5;CL<5;C*!.& ' Cevap: 190°, 280° çözüm kavrama sorusu <Q 3PQ 0$$$13 2 2 <Q &!.!&/ +<S&.#!&/& 2 <S!#$! *!.!! ' <Q ¬ <Q >Q <Q <Q *!. 2 ® 2 2 3PQ &!..* & ' 2 1. yöntem: 3PQ 35Q Q 35Q Q 2 2 º 2 ?Q N <S #!&/& ! &! ' 2 Q Q 2 2 2. yöntem: 3PQ $#(, #! &)! *!. 2 !$%!&&!#.<S&. !! ' 26 3PQ 36Q <Q 36Q <Q <Q 6Q 2 2 2 2 2 º <Q >Q Q <Q 6Q !#.<S&. ! ' 2 2 6Q Q *!.& ' 2 2 Cevap: >Q Q % 2 2 Trigonometri - 1 soru 1 soru 5 @>;'$$ =<3;C soru 2 =<<;C E=<2;C D=<>;C =<6;C =2;;C E=<>;C D=3<;C =?;C soru 4 =<>;C E=<P;C D=2;;C =22;C 1–A 2–B E=35;C D=<>;C 3–E Q 2 = Q > D= 2Q > = 6Q > E= Q < D= = 6Q ? <Q 2 Q < soru 8 =3<;C E= Q ? soru 7 = @%;;'$$ =4;C Q 5 32Q 0$$0 2 &>;'$$ =2;C = 33Q 0$$0 ? = 0NO808YAYINLARI soru 3 2Q 5 soru 6 ,%;'$$ =2<;C 2Q 0$$0 > = =2;;C Q 3; 5–E 27 6Q 2 E= >Q 2 D= <Q 2 = Q 2 = >Q 6 <5Q 0$$0 6 = 4–D = = Q 6 E= 6–A <Q 6 D= 7–B 2Q 6 8–C Trigonometri - 1 çözüm kavrama sorusu y y P 60° O 30, 60, 90 üçgenindeki oranlar P 30° 1 30° 60° x O 4$1813 2k x A 60° k y P 1 , ñ3 2 2 P ñ3 2 30° 1 kñ3 ñ3 2 60° ñ3 2 30° 1 A 2 O x 60° O A 1 2 3 2 ¬ & ' X### &! X % < < ® 1 3 ¬ Cevap: P , 2 2 ® çözüm kavrama sorusu y y P P 150° O x P 60° 30° A 150° 1 2 x O 60° A P 1 2 A ñ3 2 1 2 150° O 30° ñ3 2 O X # ' *!-& #!&/&$ -,&/ ! ' y 4$1813 1 x 2 3¬ X % < < ® 3 1 ¬ , Cevap: P 2 ® 2 28 Trigonometri - 1 y soru 1 y soru 4 P 45° O P 135° x x O 4$18- 4$18- #!* #!* 2 2 ¬ = % < < ® 3 3¬ = % < < ® 3 3 ¬ D= % < < ® soru 2 3 3¬ 2 3¬ = % = % < < ® < < ® 3 3 3 ¬ D= % = % < < ® < E= :3% 3= = :<% <= soru 5 y P 3 3 ¬ E= % < < ® 3 ¬ < ® y 30° 300° x 4$18#!* 3 2 ¬ = % < < ® 3 3 2 ¬ 2 ¬ = % E= % < < < ® < ® 2 3¬ 2 3¬ D= % = % < ® < ® < < soru 3 60° O P 4$18#!* 2 3¬ = % < < ® 2 3 3¬ 2 ¬ = % E= % < < < ® < ® 3 3 2 ¬ 2 ¬ D= % = % < < ® < ® < soru 6 y x O 0NO808YAYINLARI O y 315° x x O P P 4$18#!* 4$18#!* 3 3 3 2 ¬ 3¬ 2 ¬ = % = % E= % < < ® < ® < ® < 2 3 3 2 ¬ 2 ¬ D= % = % < < ® < < ® 3 3 3 ¬ = % = % < < ® < 3 3 ¬ D= % < < ® 1–D 2–A 3–C 4–E 29 3 ¬ < ® 3 3 ¬ E= % < < ® 3 3¬ = % < < ® 5–D 6–A Trigonometri - 1 çözüm kavrama sorusu 810$@%;'$1 y 13 y P 30° 120° ? x O X#$ P 1 60° 1 1 2 2 120° x O 3 & ' < Cevap: 1 2 çözüm kavrama sorusu y >Q 0$1 2 13 810$ >Q >'35; <>;n 2 2 240° x O ? P y X## & 240° O 30° 1 P 60° ñ3 2 2 < x ñ3 2 Cevap: 3 2 çözüm kavrama sorusu 70$@:>'$1 /13 y O ? x 135° ? P y 1 ñ2 1 ñ2 P 30 1 ñ2 45° 1 O 135° 1 ñ2 X#Q 3 $L < 3 x # &L < Cevap: 1 1 % 2 2 Trigonometri - 1 soru 1 soru 5 810$:;'$1 70$,>'$1 = 3 < soru 2 = 2 < E= 3 < D= 3 < 2 < = soru 6 810$@>;'$1 2 < soru 3 = 3 < E= 3 < D= 3 < = 2 < = 6Q 0$1 810$ 2 = 3 < soru 4 = 3 < E= 2 < D= 3 < = 3 < 1–E 2–D E= 3 < 3–E D= 3 < = 2 < = 3 < D= = 2 < E= 3 < 2 < D= = 3 < 3 < soru 8 2 < 3 < 3 < soru 7 = = E= <Q 0$12 6Q 0$1 2 3 < 3 < 70$ 810$ = = %@;'$1 0NO808YAYINLARI = 2 < = = 3 < E= 2 < D= 3 < = 2 < S0$1 2 < = 3 4–B 5–D 31 = 2 < 6–C E= 3 D= ; 7–A = 3 8–D Trigonometri - 1 Kosinüs Fonksiyonu: . ( &D.#X#!'X#$D$$& cosD!-* ! ' .#&#$#!&/&%A$&& ' . ( &! #$.S33&/ ! !!+/&#,##&/ JS3%3K !/& ' +#oJS3%3K 90° Do+#D 180° y P a 0° x (Kosinüs ekseni) O cosa 270° 1£ cosa £ 1 çözüm kavrama sorusu J;'$$$13 y P 30° 1 ñ3 60° 2 O 1 cosa x (Kosinüs ekseni) 2 3 2 ¬ 3 X # ## &! X < % < $ #!&/ ® < 3 &% +# ?;n & ' < 1 Cevap: 2 çözüm kavrama sorusu @>;'!13 60° y 30° P 1 1 150° 2 cosa ñ3 O x 2 2 3¬ X### &! X < % < ® X#$'*!-&#!&/&-,&/ ! ' +#36;n Cevap: 3 2 Cevap: 1 2 çözüm kavrama sorusu +# 2 & ' < 6Q !13 > +# 6Q 6'35;n +# +# <<6n > > y cosa 1 P 1 ñ2 225° 1 ñ2 x 45° 3 3 ¬ % X### &! X < < ® #!&/& +# B 32 3 < Trigonometri - 1 soru 1 soru 5 :;'! = 3 < = soru 2 2 < E= < < +# D= < < = 3 < 2 < < < soru 6 @:>'! = < < E= +# < < D= 3 < = 2 < 2 < = 2 < E= D= 3 < = < < = < < = 2 < = 2 < <Q ! 2 = 2 < = 3 < E= 3 < D= 2 < 0NO808YAYINLARI = Q ! > = soru 3 soru 7 %@;'! = 3 < soru 4 = 2 < E= +# 3 < D= 2 < = < < 1–B 2 < 3 < soru 8 :;;'! = 2Q ! > = = 3 < 2–C E= +# 3 < D= 3–B 2 < = < < 2 < 5–E 33 = 2 < E= < < D= < < 33Q ! ? = 4–C = 3 < 6–B E= 3 < D= 7–C < < 8–E Trigonometri - 1 y P2(0, 1) P3( 1, 1) 90°<a<180° cosa<0 180° x P1(1, 0) O y 90° 0°<a<90° cosa>0 II. bölge I. bölge III. bölge IV. bölge 0° 180°<a<270° cosa<0 270°<a<360° cosa>0 P4(0, 1) 270° JX3K#!.+#;CL3 +#D) Q JX<K#!.+#4;CL +# ; < JX2K#!.+#35;CL+#SLS3 JX>K#!.+#<P;CL +# x 2Q ; < ;CRDR4;C + 4;CRDR35;C S 35;CRDR<P;C S <P;CRDR2?;C + çözüm kavrama sorusu Q@>;' !13 y ñ3 2 1 2 +#:36;n= 30° O x 150° P 2 < Cevap: 3 2 çözüm kavrama sorusu D#!( % 2cosDS@!!!13 S3[+#D[3#!&/& S<[<+#D[< S3[<+#DM3[2 <+#DM3,&JS3%2K !/&&/ ! 'Cevap: [– 1, 3] çözüm kavrama sorusu L+#3;C L+#P;C +L+#3<;C +#3;C%+#P;C+#3<;C&/ ! . ( & ) !!' y P120 P70 120° #!&/-* %/0$$$0$!! 013 c O 70° b 10° P10 a x Z!&&-* !&/- 34 +#3<;CR+#P;CR+#3;C +RR Cevap: c<b<a Trigonometri - 1 soru 1 soru 5 D#!( % 3cosD@!!#!- T;'S@H;'S%&;' * =S< =S3 E=; D=3 =< =JS>%S3K soru 2 QJ;' ! 2 = < D=JS2%<K soru 6 < = < 3 E= < 3 D= < 2 = < =JS>%S<K L+#6;' L+#2;' +L+#P;' #!&/-* %/0$$$0$!! ##!* 0NO808YAYINLARI Q%@;' ! 2 = < < = < 3 E= < 3 D= < 2 = < =+RR D=RR+ soru 7 L+#3;;' L+#36;' +L+#3P;' Q@H;' S@H;' E=; D=3 =< =+RR D=R+R soru 8 =S3 =R+R #!&/-* %/0$$$0$!! ##!* =S< E=+RR =+RR soru 4 =JS>%<K =RR+ soru 3 E=JS<%<K E=RR+ =RR+ L+#6' L+#<6;' +L+#<4;' #!&/-* %/0$$$0$!! ##!* =+RR 1–B 2–D 3–A 4–A 5–E 35 =RR+ D=RR+ 6–B E=R+R =R+R 7–A 8–C Trigonometri - 1 Sinüs Fonksiyonu: . ( &D.#X#!'X## &D$$& sinD!-* ! ' .&## &#!&/&%$&& ' . ( & # # &.S33&/ ! !!+/&,##&/ JS3%3K !/& ' oJS3%3K 90° sina DoD 180° O y (Sinüs ekseni) P a 0° x 270° 1£ sina £ 1 çözüm kavrama sorusu :;'$$$13 y (sinüs ekseni) 60° P sina 1 1 30° 2 x O ñ3 2 2 3¬ 3 % # & X### &! X < < < ® #!&/&% 2;n 3 & ' < Cevap: çözüm kavrama sorusu @:>'!13 y (sinüs ekseni) P 1 ñ2 1 45° 1 ñ2 sina 135° x O 3 X### &! X % < X## & 3 ¬ < ® 3 3 < #!&/&% 326n < < < Cevap: çözüm kavrama sorusu 2 2 y (sinüs ekseni) 6Q !13 2 1 2 90° 6Q 6'35;n 2;;n 2 2 180° 300° sina 1 2 1 60° ñ3 2 x 270° 30° P 3 2 ¬ X### &! X % < < ® X## &'*!-&#!&/&-,&/ ! ' 36 6Q 2 2;;n 2 < Cevap: 3 2 Trigonometri - 1 soru 1 soru 5 J;'! 2 < = soru 2 = 3 < E= 3 < D= 3 < = 2 < 3 < 2 < soru 6 @%;'! = 2 < E= < < D= 3 < = 2 < = 3 < E= 3 < 2 < D= = < < 6Q ! ? = 2 < = 3 < E= < < D= 2 < = 3 < 0NO808YAYINLARI = Q ! > = soru 3 soru 7 %%>'! = 2 < soru 4 = 3 < E= < < D= < < = 3 < 1–A 2 < 2 < soru 8 %@;'! = >Q ! 2 = = 3 < 2–B E= < < 3–C D= 3 < = 2 < = 4–B = < < E= 3 < D= 3 < = 2 < 2 < = 33Q ! ? 2 < 5–E 37 = < < E= 6–E < < D= 7–A 3 < 8–E Trigonometri - 1 y (sinüs ekseni) y (sinüs ekseni) P2(0, 1) 90° 90°<a<180° sina>0 P3( 1, 0) 180° x P1(1, 0) O 0°<a<90° sina>0 II. bölge I. bölge III. bölge IV. bölge 0° 180°<a<270° sina<0 270°<a<360° sina<0 P4(0, 1) 270° JX3K#!.;CL; D) Q JX<K#!.4;CL 3 < JX2K#!.35;CLSL; JX>K#!.<P;CL x 2Q 3 < ;CRDR4;C + 4;CRDR35;C + 35;CRDR<P;C S <P;CRDR2?;C S çözüm kavrama sorusu Q¬ !13 > ® y (sinüs ekseni) O sina= 1 ñ2 1 ñ2 1 ñ2 p 4 1 x 1 ñ2 P Q¬ 3 < > ® < < Cevap: 2 2 çözüm kavrama sorusu D #! ( % DL<M3 #!&/ -* % 0 !!!13 3 b B b 3 #!&/& N 3 b < 3 b 3 < b < b ; 3 b b ; Cevap: [– 1, 0] JS3%;K !/&&/ ! ' çözüm kavrama sorusu L2;C L3<;C +L<>;C 2;C%3<;C<>;C&/ ! . ( & ) !!' y P120 a #!&/-* %/0$$$0$!! 013 240° P240 b 120° O 30° P30 x c Z!&&-* !&/- 38 <>;CR2;CR3<;C +RR Cevap: c<a<b Trigonometri - 1 soru 1 soru 5 D#!( %2sinDS:!!#!- ;'ST;'S@H;' * =S< =S3 E=; D=3 =< =J3%<K soru 2 D=J3%6K soru 6 Q¬ ! < ® =S< =J<%>K =S3 E=; D#!( %sinDU:@!0 !!!#!* D=3 =< 3 <¯ = ¡ % ° ¡¢ < 2 °± <Q ¬ ! 2 ® 3 = < < E= < < D= < 3 = < 0NO808YAYINLARI 2 = < 3¯ = ¡;% ° ¡¢ 2 °± soru 7 L3;C L6;C +L5;C Q%,;' ! 3 E= < < D= < 2 = < =+RR D=R+R soru 8 3 = < L36;C L<3;C +L22;C 3–A =RR+ #!&/-* %/0$$$0$!! ##!* 2–B E=RR+ =L+R 1–D = < ;% 2 > #!&/-* %/0$$$0$!! ##!* 2 = < <¯ E= ¡;% ° ¡¢ 2 °± =+RR soru 4 =J<%6K D= < ;% < > soru 3 E=J3%>K 4–E 5–D 39 =RL+ D=R+R 6–C E=LR+ =+RR 7–E 8–A Trigonometri - 1 Tanjant Fonksiyonu: . ( &D. JXK#!' (AL3&#/ /## & DV& tanD!-* ! '4;C<P;C!.! ! (! AL3&#/ &/. U,##S\4;C%<P;C]& ' S\4;%<P;]o DoD 1 tana y T P 1 O 1 a 1 x x=1 doðrusu (Tanjant ekseni) çözüm kavrama sorusu J;'V13 y tana 30° 2 T(1, ñ3) ñ3 P 60° O x 1 Tanjant ekseni D . ( AL3 &#/ / # 0:3% 2= 0 # # & 2 #!&/&% ?;CL2 ' Cevap: 3 çözüm kavrama sorusu 6Q !13 ? 6Q 6'35;n 36;n ? ? y P 30° 150° 1 O 1 ñ3 30° 60° 1 ñ3 x Tanjant ekseni 40 6Q 3 36;n ? 2 Cevap: 1 3 Trigonometri - 1 soru 1 soru 5 ,>'! = 2 soru 2 = 3 E= ; D= 3 2 = 3 2 = soru 6 @%;'! 3 2 = E= ; D= 3 = E= 3 3 2 D= = 2 2Q ! > = 3 2 3 2 = ; D= E= 3 3 2 = 2 0NO808YAYINLARI = 2 Q ! ? = soru 3 soru 7 %@;'! = 3 < soru 4 = 3 2 E= 3 2 D= 3 = 1–E 2 = soru 8 :;;'! = 2 6Q ! 2 = 2 = 3 2 2–A E= ; D= 3–C 2 = 3 2 3 2 5–B 41 3 2 E= 3 D= 2 = 3 2 = 3 2 33Q ! ? = 4–A = 2 6–A E= 3 D= 7–D 2 8–A Trigonometri - 1 y y P2 P3 P1 O 90° 90°<a<180° tana<0 () II. bölge I. bölge 180° x 180°<a<270° tana>0 (+) P4 III. bölge IV. bölge 270° 0° x 270°<a<360° tana<0 () Tanjant ekseni Tanjant ekseni JX3K#!.;CL; D) Q JX<K#!.4;CL ( < JX2K#!.35;CLSL; JX>K#!.<P;CL 0°<a<90° tana>0 (+) 2Q ( < ;CRDR4;C + 4;CRDR35;C S 35;CRDR<P;C + <P;CRDR2?;C S çözüm kavrama sorusu <Q ¬ !13 2 ® <Q ¬ <'35; ¬ :3<;= 2 ® 2 ® y tan(120)=ñ3 30° T ñ3 O 60° 120° x 1 P Tanjant ekseni <Q ¬ :3<;= 2 ® çözüm kavrama sorusu L2;C L6;C +L36;C Cevap: 3 2 b P150 a y 50° 150° O #!&/-* %/0$$$0$!! 013 c P50 30° P30 T50 T30 x T150 Tanjant ekseni Z!&&-* !&/-% 42 36;CR2;CR6;C +RR Cevap: c<a<b Trigonometri - 1 soru 1 soru 5 2Q ¬ ! < ® Q:;' ! = 2 soru 2 3 2 = E= ; D= 3 = =0( 2 soru 6 QT;' ! =S2 =S3 E=3 D=; =( =S3 E=; D=3 =2 L3;C L<;C +L5;C #!&/-* %/0$$$0$!! ##!* =R+R soru 3 0NO808YAYINLARI Q@H;' SQ@H;' =S< =S3 E=< D=; =( =R+R D=+RR soru 7 E=RR+ =+RR L3;;C L3<;C +L3P;C #!&/-* %/0$$$0$!! ##!* =+RR soru 4 6Q ¬ ! ? ® = 2 D=RR+ soru 8 = 3 2 E= ; D= 2 = 3 2 =RR+ E=R+R =R+R L3?;C L34;C +L<;;C #!&/-* %/0$$$0$!! ##!* =R+R 1–B 2–E 3–D 4–E D=RR+ 5–A 43 =RR+ 6–C E=R+R =+RR 7–B 8–D Trigonometri - 1 Kotanjant Fonksiyonu: . ( &D. JXK#!' (L3&#/ /#$D V& cotD!-* ! ';C35;C!.! ! (! L3&#/ &/. #U,##S\;C%35;C]& ' +# S\;C%35;C]o y 1 Do+#D y=1 doðrusu (Kotanjant ekseni) C P 1 O a 1 cota x 1 çözüm kavrama sorusu :;'V13 y C(ñ3, 1) P 60° 1 30° O ñ3 Kotanjant ekseni cot30° x 2;C!. (L3&#/ / #E:2%3=E#$2#!&/&% +#2;CL2 ' Cevap: 3 çözüm kavrama sorusu +# <Q !13 2 +# <Q <'35;n +# +#3<;n 2 2 y C P 30° Kotanjant ekseni 1 120° 60° 1 1 O ñ3 ñ3 +# 44 <Q 3 +#3<;n 2 2 x Cevap: 1 3 Trigonometri - 1 soru 1 soru 5 J;'! = 2 soru 2 = 3 2 +# E= 3 = D= ; 3 2 Q ! > =S3 =S2 soru 6 @:>'! =S3 E=; D=3 =2 E=; D=2 =3 +# 6Q ! ? = 3 2 E= 3 = ; 3 2 D= = 2 0NO808YAYINLARI =S2 soru 3 soru 7 %,;'! = 2 soru 4 = 3 2 +# E= 3 D= 3 2 = 1–B 3 2 soru 8 = 3 2 2–B = 2 E= 3 D= 2 = 3 6Q ! +# 2 ::;'! = 2 6Q ! > = 2 E= 3 3–D D= 3 2 = = 2 4–A 3 2 5–E 45 = 2 6–E E= 3 D= 3 7–E = 2 8–A Trigonometri - 1 y y P2 P3 Kotanjant ekseni P1 O 90° 90°<a<180° cota<0 II. bölge 180° x 180°<a<270° cota>0 III. bölge P4 IV. bölge 0° Kotanjant ekseni x 270°<a<360° cota<0 270° JX3K#!.+#;C( Q JX<K#!.+#4;CL +# L; < JX2K#!.+#35;CL+#S( JX>K#!.+#<P;CL +# I. bölge 0°<a<90° cota>0 +#D) 2Q L; < ;CRDR4;C + 4;CRDR35;C S 35;CRDR<P;C + <P;CRDR2?;C S çözüm kavrama sorusu QJ;' !13 y C Kotanjant ekseni 30° 1 60° O 60° 1 1 ñ3 ñ3 x P +#:?;n= L+#P;C L+#3;;C +L+#<<;C Cevap: 1 3 çözüm kavrama sorusu 3 2 y C100 C70 P100 P70 C220 220° #!&/-* %/0$$$0$!! 013 b Oa c x P220 Z!&&-* !&/-% +#3;;CR+#P;CR+#<<;C RR+ Cevap: b<a<c 46 Trigonometri - 1 soru 1 soru 5 33Q ¬ +# ? ® ! Q,>' ! =3 =2 soru 2 E=; D=S2 =S3 = 2 = soru 6 QT;' ! =( =S3 3 2 E= ; E=; D=3 3 2 E= 3 2 D= 2 = ; 0NO808YAYINLARI 6Q ¬ +# ! ? ® = =S%S%M D=S%M%M soru 7 L+#3;C L+#>;C +L+#56C #!&/-* %/0$$$0$!! ##!* =S3 =; E=3 D=2 =( =RR+ D=+RR soru 8 2Q ¬ +# ! < ® E=M%S%S =M%S%M =RR+ soru 4 2 =2 2 = @;;'@&;'%J;'#0#!* = 3 2 =S%M%S soru 3 D= E=R+R =+RR L+#54C L+#43C +L+#<?PC #!&/-* %/0$$$0$!! ##!* =RR+ 1–E 2–C 3–A 4–B D=R+R 5–E 47 =R+R 6–B E=RR+ =+RR 7–D 8–A Trigonometri - 1 Sekant ve Kosekant Fonksiyonları: . ( &D. JXK#!'D.X#& . .(!/A /#$D& D !-* ! '0//## &D & cscD !-* ! ' K y csca N#!( % P O a seca x S + S\4;CM'35;C]oS:S3%3= Do+D ++ S\'35;C]oS:S3%3= Do++D +++,##! :S3%3= !/&&/ !(' çözüm kavrama sorusu J;'/13 y csc60°= 2 ñ3 60° 2 ñ3 1 P 60° 30° O ++ ?;n sec60°=2 2 x < < 2 2 3 +?;CL<Cevap: ve 2 2 3 2 çözüm kavrama sorusu @>;'!13 y csc150°=2 30° 2 P 1 60° 150° 30° O x Cevap: 2 ++36;CL< çözüm kavrama sorusu L+26C L+>6C +L+P;C y P70 #!&/-* %/0$$$0$!! 013 O 35° P45 P35 b a sec35° c sec70° sec45° x Z!&&-* !&/-% 48 +26CR+>6CR+P;C RR+ Cevap: a<b<c Trigonometri - 1 soru 1 soru 5 :;'! = < 2 2 soru 2 = < E= ;'! 3 < 2 < D= = =3 2 < 2 = < E= 2 < D= < 2 2 = < :;'! =< E=3 D=2 =S%S%M D=M%S%S soru 7 < =M%M%S D=M%M%M soru 8 E= 3 D= < =M%M%S =< T;'! = E=S%M%S @&'@&,':;;'#0#!* < 2 = 2 =<2 =M%S%M soru 4 D=< =S%S%S 0NO808YAYINLARI =<< E=2 &%'@@;'%@:'#0#!* soru 3 =; soru 6 ,>'! = = 2 E=S%M%M =S%S%S L++<;C L++>;C +L++?;C #!&/-* %/0##!* =+RR 1–A 2–B 3–E 4–C 5–A 49 =RR+ D=R+R 6–D E=R+R =+RR 7–B 8–E Trigonometri - 1 çözüm kavrama sorusu @;>'@H@'%@:'/:@,'#- (sinüs ekseni) y 013 cot314° sin105° cotanjant ekseni tan213° cos181° x (kosinüs ekseni) tanjant ekseni 3;6C^;%+#353CR;%<32C^;%+#23>CR; M%S%M%S Cevap: +, –, +, – çözüm kavrama sorusu LP;C% L?;C +L+#>;C #!&/ -* % / 0$$$0$!!013 y b a T60 P70 P60 P40 40° x c tan ekseni Z!&&-* !&/-% +#>;CRP;CR?;C +RR çözüm kavrama sorusu L326C L6;C +L+#34;C Cevap: c<a<b y T50 b P135 #!&/-* %/0$$$0$!! 013 a cot ekseni P50 c P190 x tan ekseni Z!&&-* !&/-% 50 326CR6;CR+#34;C RR+ Cevap: a<b<c Trigonometri - 1 soru 1 soru 5 HH'@;;'%J;'#0#!* L3;C% L+#3;C% +L3P;C #!&/ -* % / 0$$$0$!!##!* =M%S%S =M%M%M D=M%S%M E=S%M%M =LR+ =M%M%S soru 2 @@;' %;;' %H;' # 0 #!* =S%M%M D=L+^ soru 6 =M%M%S D=S%S%M 0NO808YAYINLARI =S%S%M D=S%M%M soru 7 D=S%S%M%S 2–D E=+RR =RR+ L36;C%L+#36;C%+L+#2?6C#!&/-* %/ 0$$$0$!!##!* E=S%S%S%S =RR+ =S%M%M%S 3–A =R+R D=+RR soru 8 >Q 6Q 2Q 33Q # % +# % % +# 2 ? > 2 0#!* 1–E =RR+ =+RR E=M%S%S =M%S%M =S%S%S%M E=RR+ L+#26C%L<6C%+L+#<;C#!&/-* %/0 $$ $0$! ! # #!* =S%M%S%S =R+R D=+RR soru 4 =RR+ =S%M%S @>;'%;>':%;'#0#!* =RR+ E=M%S%S =S%M%S E=L+R LP;C%L+#P;C%+L+#P;C#!&/-* %/0 $$ $0$! ! # #!* soru 3 =L+R 4–C D=+RR 5–B 51 =R+R 6–D E=RR+ =+RR 7–A 8–C Trigonometri - 1 çözüm kavrama sorusu y y P 1 T P sina a O tana T a x & . ( & D . !) ' 8 / W D.+&% D0113 X#X:+#D%D= x cosa 1 O 0#0:3%D= çözüm kavrama sorusu y y K P S T C P S(sina) a O K(tana) 1 T a x O C(cosa) 1 T K P S tana sina x O cosa C 1 0 !!L3'DSD'+#D & . ( &D. !) 'D13 < LDSD'+#D & ' Cevap: tanD – sinD.cosD çözüm kavrama sorusu y K y K 1 P a N C O P 1 x 1 sina a N(cota) C(cosa) O & . ( &D. !) 'D13 0 !!L K x sina N C cosa O cota 3': +# B = B: +# B = < < +# B B'+# B < < Cevap: 52 P 1 cotB sinB .cosB 2 Trigonometri - 1 soru 1 soru 4 y 90° y 90° P P a 180° 0° O a 180° x A 270° 0° B x 270° & . ( & D . !) ' 8 & . ( &D. !) '#- #!* !*# =:D%+#D= =+#D =:+#D%D= D=:D%+#D= soru 2 E=:+#D%SD= =:+#D%D= y a & . ( &D. !) 'W#!* =:D%+#D= D=:SD%3= y E=:3%D= = B'+# B < soru 6 90° C O a A 0° B x & . ( &D. !) '68$#!*# =:3%+#D= y P 270° = B'+# B D= soru 3 90° 180° x=1 E=+#DSD =3M+#D x T =:+#D%D= =S+#D D=3S+#D soru 5 0NO808YAYINLARI +# B < E= B < = <' B'+# B y 90° y=1 C y=1 T a 180° 0° 180° x O 270° 270° & . ( &D. !) '#!* =:+#D%3= 1–B =:3%+#D= D=:D%3= 2–C a A 0° B x x=1 & . ( &D. !) 'W#!*# E=:3%D= = =:+#D%3= 3–A +# B B < +# B B E= +# B B < +# B ' B D= B +# B = < 4–D 53 = 5–C 6–A Trigonometri - 1 y P2 1 P1 JX<K#!.:35;CSD=& +& '&X3E3 X<E< .-! ) .-! #!&/ -* !& ' & 1 1 a a C2(cos(180° a)) O C1(cosa) &#!% x +#:35;CSD=LS+#D& ' ( )!&)/&.&*)! $! (' 1 +#:35;CSD=LS+#D p +#:35;SD='*!-& :S=&/ !&/. +#:35;C+D=LS+#D p +#:35;MD='*!-& :S=&/ !&/. :35;CSD=LMD p :35;SD='*!-& :M=&/ !&/. :35;CSD=LSD p +#:35;CSD=LS+#D p :35;C+D=LSD p :35;SD='*!-& :S=&/ !&/. :35;C+D=LMD p :35;MD='*!-& :S=&/ !&/. +#:35;SD='*!-& :S=&/ !&/. :35;MD='*!-& :M=&/ !&/. +#:35;C+D=LM+#D p +#:35;MD='*!-& :M=&/ !&/. +:35;CSD=LS+D+:35;CMD=LS+D ++:35;CSD=LM++D++:35;CMD=LS++D çözüm kavrama sorusu @%;'#13 +#:3<;C=L+#:35;CS?;C=#! ,&&!! ' 3 +#:35;CS?;C=LS+#?;CL & ' < p +#3<;C%'*!-& :S=&/ !&/& +#3<;n 3 < Cevap: 1 2 çözüm kavrama sorusu @&;'/%>;'#13 3P;CL:35;CS3;C=LM3;C p 3P;C%'*!-& :M=&/ !&/& <6;CL:35;CMP;C=LSP;C p <6;C%'*!-& :S=&/ !&/& Cevap: sin10°, – sin70° çözüm kavrama sorusu @,;'/%:;'#13 3>;CL:35;CS>;C=LS>;C +#<2;CL+#:35;CM6;C=L+#6;C Cevap: – tan40°, cot50° 54 Trigonometri - 1 soru 1 soru 5 @J;'##!* =<;C =S<;C D=S+#<;C soru 2 %;;'##!* E=+#<;C =<;C =?;C @:;'##!* =S+#2;C D=+#6;C soru 3 E=+#2;C = =S+#6;C @@;'##!* =S3;C =3;C D=P;C soru 4 E=SP;C 1–A 2 < soru 7 soru 8 @J;'##!* D=S<;C 2–E = 3 < < < D= < 2 2 D= E= 3 < = 2 < = < E= < = < %%>'! E=<;C = =S+#?;C 3–C = < =S<;C =+#<;C =S+#3;;C %,;'! =S+#<;C E=S+#<;C %@;'! 0NO808YAYINLARI =+#<;C D=+#P;C soru 6 =6;C 4–A < 2 2 5–C 55 = < 6–B E= < D= 7–A < = < 2 2 8–C Trigonometri - 1 y O a a +#:2?;CSD='*!-& :M=&/ !&/. +:2?;CSD=LM+D p +:2?;CSD='*!-& :M=&/ !&/. X3X<.-! ).-! #!&/-* !& ' A B cosa x &&#!% +#:2?;CSD=L+#D& ' ( )!&)/&.&*)! $! (' sina +#:2?;CSD=LM+#D p JX<K#!.:2?;CSD=:SD=& +& '& P1 sina P2 :2?;CSD=LSD p :2?;CSD=LSD p :2?;CSD='*!-& :S=&/ !&/. :2?;CSD='*!-& :S=&/ !&/. +#:2?;CSD=LS+#D p +#:2?;CSD='*!-& :S=&/ !&/. ++:2?;CSD=LS++D p ++:2?;CSD='*!-& :S=&/ !&/. +#:2?;CMD=.&2?;C*!.;C#!&/&+#:2?;CMD=L+#D( )!& :2?;CMD=LD%:2?;CMD=LD%+#:2?;CMD=L+#D%+:2?;CMD=L+D++:2?;CMD=L++D& ' çözüm kavrama sorusu :,;'#13 +#:2?;CSD=L+#D#!&/&% +#2>;CL+#:2?;CS<;C=L+#<;C& ' Cevap: cos20° çözüm kavrama sorusu %T;'/:&;'#13 :2?;CSD=LSD#!&/&% <4;CL:2?;CSP;C=LSP;C +#:2?;CMD=L+#D#!&/&% +#2P;CL+#:2?;CM3;C=L+#3;C Cevap: – sin70°, cos10° çözüm kavrama sorusu :;;'/:@>'!13 :2?;CSD=LSD#!&/&% 2;;CL:2?;CS?;C=LS?;CLS2 +#:2?;CSD=LS+#D#!&/&% +#236CL+#:2?;CS>6C=LS+#>6CLS3 Cevap: – 3, – 1 çözüm kavrama sorusu :;;'!13 +:2?;CSD=L+D#!&/&% +2;;CL+:2?;CS?;C=L+?;CL< Cevap: 2 56 Trigonometri - 1 soru 1 soru 5 :@;'##!* =S+#6;C =+#6;C D=S6;C soru 2 :@>'! E=6;C = =+#3;C :,;'##!* =<;C D=+#>;C soru 3 E=S<;C =6;C D=S3;C soru 4 1–B 2 < E=3;C soru 7 2–C 2 E= < D= 3 = 3 < =<2 E=< D=3 =; =+#3;C soru 8 2 2 = =<2 = = 3 ,;>'S,;>' :;;'! = D= < = < 2 :>;'##!* < 2 2 =S+#>;C =S6;C E= :T;'S,%;' 0NO808YAYINLARI = < < soru 6 =>;C E= :T;'S,%;' 2 D= 2 3–D = 2 2 = 4–E > 2 2 5–A 57 = < 2 2 6–D E= 2 < D= 7–C 2 = < 2 8–A Trigonometri - 1 y P2 B P1 JX<K#!.:4;CMD=& +& 'X3.-! X<.-).-! & ' a a O x A &&#!% +#:4;CMD=LSD& ' ( )!&)/&.&*)! $! (' +#:4;C+D=LSD p +#:4;CMD='*!-& :S=&/ !&/. +:4;C+D=LS++D p +:4;CMD=%'*!-& :S=&/ !&/. :4;C+D=LM+#D p :4;C+D=LS+#D p :4;CMD='*!-& :M=&/ !&/. :4;CMD='*!-& :S=&/ !&/. +#:4;C+D=LSD p +#:4;CMD='*!-& :S=&/ !&/. ++:4;C+D=LM+D p ++:4;CMD='*!-& :M=&/ !&/. 4;C!.! !!-!& *+,3?&!-! (-* % :4;CSD=L+#D%+#:4;CSD=LD%:4;CSD=L+#D%+#:4;CSD=LD%+:4;CSD=L++D++:4;CSD=L+D& ' Uyarı .! :4;_D=#! ,&/(& -## ,##o+#%+#o%o+#%+#o%+o++% ++o+#! &/)/&&(' çözüm kavrama sorusu @&;'#13 :4;CMD=L+#D#!&/&% 3P;CL:4;CM5;C=L+#5;C& ' Cevap: cos80° çözüm kavrama sorusu @;;'#13 +#:4;CMD=LSD#!&/&% +#3;;CL+#:4;CM3;C=LS3;C& ' Cevap: – sin10° çözüm kavrama sorusu @>;'S@:>'13 :4;CMD=LS+#D#!&/&% 36;CL:4;CM?;C=LS+#?;CL 3 2 +#:4;CMD=LSD#!&/&% +#326CL+#:4;CM>6C=LS>6CLS3 3 S3& ' 36;CM+#326CL 2 58 Cevap: 1 1 3 Trigonometri - 1 soru 1 soru 5 @@;'##!* =3;C =+#3;C D=+#<;C soru 2 @%>'##!* E=<;C =<6C =S3;C @&;'##!* =S+#5;C D=+#5;C soru 3 E=5;C @%;'S@>;' =2 E=; D=S2 soru 7 =S<2 T>'##!* 1–D D=+#6C 2–A =++36C =+36C D=S+36C soru 8 =S+#6C E=++66C =+>6C @;>'##!* =S6C =S+66C D=+66C soru 4 =S26C =S++66C =P;C =<2 E=26C @,>'##!* 0NO808YAYINLARI =+#26C D=S+#26C soru 6 =S5;C E=S++36C =+6C @:>'S@:>' E=6C =S< =S3 E=; D=3 =< =36C 3–C 4–B 5–E 59 6–A 7–B 8–A Trigonometri - 1 y P1 JX<K#!.:<P;CSD=& +& ' JX2K a O aa P2 +#:<P;CSD=LSD p +#:<P;CSD='*!-& :S=&/ !&/. :<P;CSD=LM+#D p :<P;CSD=%'*!-& :M=&/ !&/. +:<P;CSD=LS++D B x A #! . :<P;CMD= & +& ' X3 .- ! X< .- X2.-! ).-! & ' &&#!)/&)!! (!! ' P3 +#:<P;C+D=LMD p :<P;CSD=LS+#D p +#:<P;CMD='*!-& :M=&/ !&/. :<P;CSD='*!-& :S=&/ !&/. +#:<P;CSD=LMD p :<P;C+D=LS+#D p :<P;C+D=LS+#D p :<P;CMD='*!-& :S=&/ !&/. +:<P;C+D=LM++D +#:<P;CSD='*!-& :M=&/ !&/. :<P;CMD='*!-& :S=&/ !&/. +#:<P;C+D=LSD p ++:<P;CSD=LS+D +#:<P;CMD='*!-& :S=&/ !&/. ++:<P;C+D=LS+D Uyarı .! :<P;C_D=#! ,&/(& -## ,##o+#%+#o%o+#%+#o%+o++% ++o+#! &/)/&&(' çözüm kavrama sorusu %>;'/%;;'#13 :<P;CSD=LS+#D#!&/&% <6;CL:<P;CS<;C=LS+#<;C +#:<P;CSD=LSD#!&/&% +#<;;CL+#:<P;CSP;C=LSP;C Cevap: – cos20°, – sin70° çözüm kavrama sorusu %T;'/:@;'#13 :<P;CMD=LS+#D#!&/&% <4;CL:<P;CM<;C=LS+#<;C +#:<P;CMD=LD#!&/&% +#23;CL+#:<P;CM>;C=L>;C Cevap: – cos20°, sin40° çözüm kavrama sorusu %,;'/:;;'#13 :<P;CSD=L+#D#!&/&% <>;CL:<P;CS2;C=L+#2;CL2 +#:<P;CMD=LSD#!&/&% +#2;;CL+#:<P;CM2;C=LS2;CL 60 3 2 Cevap: 3, 1 3 Trigonometri - 1 soru 1 soru 5 %:;'##!* =+#2;C soru 2 :;>'##!* =+#>;C D=>;C E=S+#>;C =6C =S>;C %J;'##!* =+#3;C D=S3;C soru 3 E=3;C 3 2 < = D= soru 4 3 2 < 3 2 < 1–C =S<6C 2–D =S++6C D=+6C soru 8 D=S+#<6C E=+5;C =++6;C E=S+6C =+?6C = 3 %,>'##!* soru 7 =++6C =>6C =S++5;C D=S+5;C %J>'##!* E= 2 =26C =++5;C =+#?;C :;;'S:;;' = E=S+#26C :>;'##!* 0NO808YAYINLARI =+#26C D=S26C soru 6 =S+#3;C %,;'! E=<6C =3 =S2 E=S3 D=S< =S<2 =+#<6C 3–B 4–E 5–D 61 6–A 7–C 8–D Trigonometri - 1 çözüm kavrama sorusu %,;'!13 <>;CL:35;CM?;C=LS?;CL 2 < <>;CL:<P;CS2;C=LS+#2;CL 2 < Y*(&-* !&/-% <>;CL:35;CM?;C=L:<P;CS2;C=& ' Cevap: 3 2 çözüm kavrama sorusu @@,;'!13 33>;C*!.!(- ' 33>;C2?;C S3;5;C2 ?;C *!. 33>;CL?;CL2 Cevap: 3 çözüm kavrama sorusu H&;'!13 5P;C*!.!(- ' 5P;C2?;C SP<;C< 36;C *!. +#5P;CL+#36;CL+#:4;CM?;C=LS?;LS2 Cevap: – 3 çözüm kavrama sorusu <2;CL:35;CM6;C=LS6;C %:;' %T;' #13 @:;' %>;' +#<4;CL+#:2?;CSP;C=L+#P;C 32;CL:35;CS6;C=L6;C +#<6;CL+#:35;CMP;C=LS+#P;C <2;C +#<4;C 6;n +# P;n = 32;C +#<6;C 6;n +# P;n 62 : 6;n +# P;n= : 6;n +# P;n= 3 Cevap: – 1 Trigonometri - 1 soru 1 soru 5 :@;'##!* =S>;C =>;C D=3;C soru 2 &>;'SH,;' E=S+#6;C =< =3 soru 6 =P;C =SP;C D=S+#P;C E=+#P;C = =3;C 0NO808YAYINLARI =S3;C D=S+#3;C soru 4 2 3? = 1–B soru 7 soru 8 3 2 2–A 2 2 E= = 2 < < 2 2 =S3 E=3 D=< =< =+#3;C = 2 > =S< E=3;C ,;>' ,%;' = 3 =S< >;;'3J;;' %%;'3%,;' ,J;'##!* =?;C D=S3 @>;'3%,;' ,%;'3@@,;' D= soru 3 E=; =+#3;C @@;'##!* E= 2 &,;' S @@;' S &J>' :&;' S @T;' S @@%>' D= 3–E 3 < =S< = < 4–C 5–C 63 =S3 E=; 6–A D=3 7–B =< 8–D Trigonometri - 1 'Q ¬ B B .& (!&/& D + #! &/( . &*)! & +& .! . & -. !& ' . 2 ® -## ,##&/) %:S_=.&(!&/& -## ,##! '8) ) !,###*!-&!&/&/ -* ! ! ' #!( % k'#!( % Q ¬ ' B B B +# B% 2 ® Q ¬ +# ' B B B B 2 ® :S_D=L_D +#:S_D=L_+#D Q ¬ ' B B B +# B% 2 ® Q ¬ +# ' B B B B 2 ® :S_D=L_D cot:S_D=L_+#D Q ¬ + ' B B B ++ B% 2 ® Q ¬ ++ ' B B B + B 2 ® +:S_D=L_+D ++:S_D=L_++D çözüm kavrama sorusu 5Q ¬ Q¬ Q 1 Q &% 4 ® 4® 4 2 5Q ¬ sin #13 4 ® 5Q ¬ 3Q Q ¬ Q 1 +# 4 ® 2 4® 4 2 Cevap: 1 2 çözüm kavrama sorusu 3Q ¬ Q ¬ B /Q%SD sin B , cos(S+D), 2 2 ® ® #13 Q ¬ B +# B 2 ® +# Q B +# B 3Q ¬ B +# B 2 ® cot 2Q B cot B Cevap: cosD, – cosD, cotD, – cotD çözüm kavrama sorusu 15Q ¬ B /QTS+D #13 cos 2 ® 15Q *!.!!' 2 Q Q 3Q 15Q 14Q Q 7Q 6Q Q 2 2 2 2 2 15Q ¬ 3Q ¬ B +# B B +# 2 ® 2 ® 9S*!.!!' 9Q 8Q Q Q :4S+D=L:S+D=LD Cevap: – sinD, tanD 64 Trigonometri - 1 soru 1 soru 5 Q Q¬ cos ! 2 3 ® Q ¬ tan B ##!* 2 ® 3 = < 2 = < < E= < 3 D= < soru 2 Q ¬ = +# B E= +#:Q B = < ® Q ¬ 2Q ¬ D= B = +# B < ® < ® = :Q B = 2 = < soru 6 Q¬ sin2Q ! 4® 3 < = D= soru 3 sin(10S+D ##!* < < E= 2 < = =D 2 < 3 < =SD D=S+#D E=+#D =+#<D 0NO808YAYINLARI = soru 7 sin(S+D ##!* 13Q ¬ B ##!* cot 2 ® =D =<D =D D=SD soru 4 E=+#D =S+#D 1–B B < D=SD E=+#D =D soru 8 3Q ¬ B + cos Q B sin 2 ® 9Q ¬ B cos 20Q B + sin 2 ® 3Q ¬ B ##!* cos 2 ® = =S+#D = +# B D= +# B 2–B E= B =S3 = B 3–D 4–E 5–C 65 =3 E=D 6–A D=+#D 7–E =SD 8–A Trigonometri - 1 , ,###!( %,:SA=LS,:A=) /!,##! tek fonksiyon& - ,! # U-* ' ,:SA=L,:A=) /!,##! .,,##& - ,! -* ' # ,##! ,:SA=L,:A= ) /!&/& ., ,##! & ' D # *!! & - ,! +!&/& - ,! -* #!&! -* !+ ' % U% #U # ,##! ,##! & ' +#:SD=L+#D :SD=LSD +#:SD=LS+#D +:SD=L+D :SD=LSD ++:SD=LS++D çözüm kavrama sorusu +#:S?;C= +#,##.,,###!&/&% !13 +#:SD=L+#D& ' +#:S?;C=L+#?;CL 1 & ' 2 Cevap: 1 2 çözüm kavrama sorusu ,##,###!&/&% 2Q ¬ sin 3 ® :SD=LSD& ' 2Q ¬ 2Q sin sin 3 ® 3 !13 sin 2S 3 L3<;CL:35;CS?;C=L?;CL 3 2 2Q ¬ 2Q 3 sin sin 3 ® 3 2 Cevap: 3 2 çözüm kavrama sorusu +#.,,###!&/&% : ='+#: = : ='+#: = +#:S=L+#:S= ,###!&/&% !13 :S=LS:S= : ='+#: = : ='+#: = 1 : ='+#: = : ='+#: = Cevap: – 1 66 Trigonometri - 1 soru 1 soru 5 Q¬ + 4 ® :S2;C= !#!* = 1 2 = 2 2 3 2 E= D= 1 2 ! = =S< 3 2 soru 2 1 2 E= 1 2 D= 2 2 = !#!* = 2 E= 2 D= 3 = 3 3 2 0NO808YAYINLARI = 3Q ¬ 4 ® = E= ; D= 1 2 = 3 3Q ¬ B ':B <Q= 2 ® 3Q ¬ B ':<Q B = 2® =3 E=; D=S3 =S< D=S< =S3 soru 8 D+EL2?;C#!( % +#:S<3;C= 2?;q E '+#: E= 2?;q D '+#:D 2?;q= !#!* = 1 3 E= 2 D= 2 = 1 3 # =3 1–A 1 2 3 3 soru 4 = 3 = soru 7 =< =< soru 3 = 3 D=< : 36q='+#:P;q='+#: 3;q= :36q='+#: P;q='+#:3;q= !#!* 3 2 E=S3 soru 6 Q¬ +# ? ® = =S< 2–E 3–D 4–C =; 5–D 67 E=< 6–E 7–B 8–A Trigonometri - 1 çözüm kavrama sorusu #!*>;'0#! ' +#23;CL+#:2?;CS6;C=L+#6;C ' +#23;C ' 3>;CL:4;CM6;C=L+#6;C ' 3>;C ' +#:S6;C=L+#6;C:.,,##= ' +#:S6;C= ' S+#<2;CLS+#:35;CM6;C=LS:S+#6;C=L+#6;C ' S+#<2;C ' 2<;CL:<P;CM6;C=LS+#6;C ' 2<;C 2<;C,&+#6;C)&/!& ' Cevap: sin320° çözüm kavrama sorusu : 36;q='+#: 326q= : 236q='+#: <>;q= :S36;C=LS36;CLS:35;CS2;C=LS2;CLS 1 2 1 2 :S236C=LS236CLS:2?;CS>6C=LS:S>6C=L>6L3 1 +#:S<>;C=LS+#<>;CLS+#:35;CM?;C=LS+#?;CL 3 +#:S326C=L+#326CL+#:35;CS>6C=LS+#>6CLS !13 1 1 ¬ 1 ' 2 :36;n='+#:326n= 2 ® 2 2 2 ? 1 1 :236='+#:<>;n= > 2 2 3': = 3 3 Cevap: 6 4 çözüm kavrama sorusu y y cos( q) x O q O q sin(q) P 8 #! * ! x P(cos( q),sin( q)) +#:ST=L+#T:ST=LST#!&/&% X:+#T%ST=& ' ' X:+#T%ST= ' X:+#T%ST=## &! & ' ' X:+#:ST=%:ST== ' X:+#:ST=%:ST==LX:+#T%ST= ' X:+#:<SST=%:S+T== ' X:+#:<SST=%:S+T==LX:+#T%ST= ' X:+#:SST=%:SST== ' X:+#:SST=%:SST==LX:S+#T%T= X### &! &/!& ' Cevap: P(cos(S – T), sin(S – T)) 68 Trigonometri - 1 soru 1 soru 6 #!*@;'0#! y 90° P 8 =3P;C =S26;C E=+#5;C 180° #! D=+#<5;C=:S3;C= a 0° O x *! 270° = : +# B% B = = :+# B% :B == Q ¬¬ D= +#:Q B =% +# B 2 ®® E= : +#:B =% B = soru 2 3Q ¬ ¬ = B % :Q B = ® 2 ® #!*%;'0# =S+#2>;C =<4;C E=<6;C D=+#:S<;C==+#:3?;C= soru 7 soru 3 y 90° 8 =:S>;C= =3>;C D=+#23;C=+#6;C E=+#32;C 0NO808YAYINLARI #!*:%;'0#! 180° #! 0° O a x * P 270° 3Q Q ¬ 3Q ¬¬ ¬ Q ¬¬ = B % +# B = B % +# B 2 ® 2 ®® ® ®® 2 2 E= :+#:Q B =% :Q B == D= :+#:B =% :B == = : +# B% B = soru 4 : 3<;q='+#: 36;q= : 326q= # soru 8 = 3 4 = 3 2 E= 3 4 D= 3 2 = 3 4 y 90° 8 180° #! 0° O x a *! P 270° soru 5 = : B% +# B = Q ¬ 3Q ¬¬ E= +# B % B 2 ® 2 ®® :S<3;C=M+#:S?;C= = < 2 1–E = 2 3 3 2–D E= < 3–E D= ; = ::B =% +# B = D= ::Q B =% +#:Q B == Q ¬ 3Q ¬¬ = +# B % B 2 2 ® ®® = < 4–E 5–B 69 6–B 7–E 8–A Trigonometri - 1 D .! -## # ! & !&/&&/ # ! !& *+*/ )'.& .#! &&/ -## &/ ! !.&.-.(! %.!&/*!-&! ) $! $! ' çözüm kavrama sorusu D.& .-&)!$ &.-.((' 4;CRDR35;C#!( % sin D A 3 6 o!&/-* %D, tanD/D!13 5 a B 4 % D 6 +# D 3 4 3 +# D > C 4 2 +D.'*!-&#!&/&% y 90° cosa<0 tana<0 cota<0 180° 0° O x 270° 4 % D 6 +# D 3 +# D > 4 ' 2 4 3 4 Cevap: % % 5 4 3 çözüm kavrama sorusu 35;CRDR<P;C#!( % +# D D . & . - &)!$ & .-.((' A 6 13 ol&/-* %sinD, tanD/D!13 13 12 D 3< % D 32 3< +# D 6 6 3< a 5 B C +D.'*!-&#!&/&% y 90° 180° sina<0 tana>0 cota>0 D 70 3< % D 32 0° O x 270° 3< +# D 6 6 3< Cevap: 12 12 5 % % 13 5 12 Trigonometri - 1 soru 1 soru 5 SRDR 4;CRDR35;C#!( % sin D 1 6 #!&/-* %D! = 2 6 = 1 6 E= 1 2 3S #!( % 2 3 sin D 6 #!&/-* % tanDSD D= 2 6 = 1 3 = soru 2 1 2 = 1 6 E= 1 <; D= 1 <; = 31 <; = < soru 6 S RDRS#!( % 2 2 D 3 SRDR 3S #!( % 2 DL2 #!&/-* % sinDSD! #!&/-* % sinD! 2 13 = E= 1 13 D= 1 13 2 = 13 soru 3 4;CRDR35;C#!( % = 0NO808YAYINLARI = 3 13 < 3; 6 = E= < < < D= < < soru 7 <P;CRDR2?;C#!( % +#DLS<2 sin D #!&/-* % sinD3D 5 3P #!&/-* % tanD! = 2 2 4 = 2 2 2 E= 2 2 D= 2 < = 2 3 2 = soru 4 +# D 1–D 36 5 E= 3P 5 D= 5 36 = 36 5 3S RDR<S#!( % 2 1 +# D 2 P <6 % = <> P 2–B E= P <> D= 3–A % #!&/-* % sin D D #!&/-* % tanD! P <> = soru 8 35;CRDR<P;C#!( % = 5 36 <6 P = <> P = 4–E 3 6 5–C 71 = 1 6 6–A E= 1 6 D= 7– A 3 6 = 4 6 8– D Trigonometri - 1 çözüm kavrama sorusu ;RDR Q ¬ B +# B #!&/&% 2 ® S #!( % 2 4 +#DL 6 Q ¬ 4 B & ' < ® 6 S ¬ #!&/-* % sin + D 13 % ® 4 5 Cevap: çözüm kavrama sorusu A S RDRS#!( % 2 DLS< :S+D=LSD DLS<#!&/&% 2 sin D 6 #!&/-* %sin(S+D 13 ñ5 2 a B C 1 y 90° sina>0 180° D . ' *!-& #!&/&% sin D 0° O x :S+D=LSDL 2 5 çözüm kavrama sorusu 2 6 Cevap: 270° SRDR 2 6 3S #!( % 2 6 +#DL 13 A +# D D :Q ¬ #!&/ -* % sin(Q + B )+ tan B % ® 13 13 6 13 3< % D 32 3< +# D 6 6 3< 12 a B 5 C +%D.'*!-&#!&/&% y 90° 180° sina<0 tana>0 cota>0 0° O 270° 3< 3< 6 % B +# B 32 6 3< 12 ¬ 12 :Q B = B 13 ® 13 2Q ¬ 6 B +# B 2 ® 12 2Q ¬ 3< 6 <;4 :Q B = B < ® 32 3< 36? B x Cevap: 72 209 156 Trigonometri - 1 soru 1 soru 5 ;CRDR4;C#!( % 4;CRDR35;C#!( % 1 2 sin D +# D #!&/-* %QSD 24 <6 #!&/-* %QS+D 3QSD 3 = 2 2 = 2 1 E= 2 1 D= 2 3 = 2 = soru 2 sin D :S ¬ old/-* % sin D % ® = 1 2 E= 1 2 D= 2 2 3 2 = soru 3 ;CRDR S #!( % 2 3 +# D 6 S ¬ #!&/-* % tan + D % ® = > 3 = 2 4 E= 2 4 D= > 3 = 6 4 = <> <6 4 6 4 2 = 3 > E= 4 2 D= 3 > = 3 6 soru 7 3S #!( % 2 +#DL3 S ¬ #!&/-* % S D 3: %S D = % ® SRDR 3 2 = 1 2 E= 2 2 D= 3 2 = 3 2 <P;CRDR2?;C#!( % 1 2 :S ¬ S ¬ #!&/-* % D S D % ® 2 ® sin D #!&/-* % sin(SD = < 6 6 E= 6 6 D= 6 6 = < 6 6 = 1–A <6 <> D= soru 8 S RDRS#!( % 2 DLS< 2 6 6 = = soru 4 = P <> :S ¬ #!&/-* % S D % ® 0NO808YAYINLARI 3 2 E= 35;CRDR<P;C#!( % DL3 = <> P = soru 6 ;CRDR4;C#!( % P <6 2–B 3–B 4–B 2 3 3 5–E 73 = 3 3 E= 6–C 3 2 D= 3 2 7–D = 2 3 3 8–E Trigonometri - 1 çözüm kavrama sorusu D 3 2 DL 3 #!&/&% 2 A % #!&/-* %sin DSD13 ò13 3 a 2 B 3 D 13 D +#DL C 3 13 2 WDQMDQW LOH D\QÜ EÐOJHOHUGH D\QÜ LíDUHWH VDKLS ROGXðXQGDQ 3 SR]LWLIGLU 2 ¬2 < 4 < 62 2 B +# B 13 ® 2 32 2 24 Cevap: çözüm kavrama sorusu 53 39 AL :2?;CSA=LSALS #!&/ -* % Q:J;'9 SQ%&;'9 !13 +#:<P;CSA=LSALS :2?;CSA=M+#:<P;CSA=LSM:S=LS< Cevap: –2a çözüm kavrama sorusu :34PC=L:35;CM3PC=L3PCL 3PCL Q@T&' Q:,:' #!&/-* % Q%>:' S@ :2>2C=L:2?;CS3PC=LS3PCLS +#:<62C=L+#:<P;CS3PC=L3PCL d!13 34Pq 2>2q +# <62q 3 : = 3 < 3 Cevap: 74 2a a +1 Trigonometri - 1 soru 1 soru 5 AL< AL % % :S ¬ o!&/-* % Q S S 9 S 9 % ® #!&/-* % sin 9 9 = > 6 = 2 6 E= < 6 3 6 D= sind!#!* 6 6 = =S< soru 2 4 3 % #!&/-* %9S 9 = 3>3 3;; E= 324 3;; D= 322 3;; = 3<4 3;; soru 3 E= 1 < D= 1 > E= D=3 =< <6CL #!&/ -* % = 1 5 soru 4 = E=; D=S3 =S< soru 8 +#AL #!&/-* % !#!* = 2–C E= a 2 D=; 3–C +#22CL % >&' @ %@:' @,&' !#!* S ¬ #!&/-* % Q S 9 S 9 % ® 1–B =< soru 7 =< =< Q%S 9 S Q S 9 \ :S ¬ S 9 % ® %;>' S ::>' J>' !#!* % = 3 =S< #!&/-* %D D = !#!* DL3 = < D=; AL ol&/-* % 0NO808YAYINLARI 3>2 3;; a 2 soru 6 +# A = E= =S =S = 4–D 1 a 1 5–A 75 = % a 2 E= 6–E a 1 a D= a 1 a 7–E = a 1 a 1 8–D Trigonometri - 1 Trigonometrik Özdeşlikler y & . ( &-* !D.# X## &! X:+#D%D=& ' P (cosa, sina) 2 2 . &!A +y L3#!&/&% O 2 a 2 x 2 2 2 2 +# D+sin DL3 2 & ' 2 +# D+sin DL3)!/&%+# DL3S D DL3S+# D)!! (!! ' D.-& .U#U.% DL )& (!/ #)& (!/ % +#DL #)& (!/ )& (!/ )!! !)' Karþý dik kenar uzunluðu Hipotenüs uzunluðu Karþý dik kenar uzunluðu sina = tana= = yazýlabilir. Komþu dik kenar uzunluðu cosa Komþu dik kenar uzunluðu Hipotenüs uzunluðu +# D sin D ( .&% +# D D'+# D D D +# D ' +# D D 1 +# D +# D sin B +# B & ' 3 D'+#DL3 & ' 1 &)!!&&! ' D çözüm kavrama sorusu B 2 2 2 L3S ?>CL+# ?>C L3S ?>C 2 2 L3S+# ?>C 2 L3S+# ?>CL ?>C 2 #!&/-* %S13 2 ML+# ?>CM ?>CL3& ' Cevap: 1 çözüm kavrama sorusu 2 2 sin 3PCM P2C P2CL+#3PC:0! .! #!&/&= 2 13 2 2 2 sin 3PCM P2CL 3PCM+# 3PCL3 Cevap: 1 çözüm kavrama sorusu 2 2 sin DME'+#EM+# D 2 2 2 sin DME'+#EM+# DL D +#2 D E '+# E 13 1 1 L3M3L< Cevap: 2 76 Trigonometri - 1 soru 1 soru 5 #!*@#! 2 2 = M+# 2 2 E= ?CM+# ?C 2 2 #!#*0# 1 +# 6;q E=A'+#AL3 2 = ?2CM+# ?2C D= P;CM <;C 2 2 2 = >;CM+# 6;C Q ¬ = B ' B 3 2 ® D=+#A'AL+#A =>;CL =A'+#ALA soru 2 soru 6 % #!* 9# #!#*0# 2 2 = 3;CL3S+# 3;C 2 2 E= <;CL3M+# <;C 2 2 =+# S3LS a D=S3M ALS+# A 2 2 2 2 = A' A =:3SA=:3MA= E=+# A' A 2 2 2 D=3S A= A'+# A 2 2 2 soru 3 % #!* ,;'0#! 2 2 0NO808YAYINLARI =:3SA=':3MA=L+# A 2 =3S+# >;C =3S 6;C E=3S+# :3>;C= 2 2 D=3S >;C=3S :32;C= soru 7 #!#*! =66CL 2 1 +# <6q 2 E=+# 6CS3L 6C 2 2 2 = <6CL3S+# ?6C D= 3;q' 1 34;q 3 2 = 353CM+# 43CL3 soru 4 soru 8 #!*@#! =A'+#A D= 1–E =3;C'5;C #!#*0# E= <6q +# ?6q 2 3–D 2 2 2 =3M+# AL AM<+# A 2 6q =+#'+#:4;CS= +# 6q 2–C 2 = >AS3LS+# >A E=><CM3L<S+# 25 D=36C'+#346CL3 1 =+#6;CL 6;q 4–D 5–A 77 6–E 7–D 8–C Trigonometri - 1 #,##! & *+ . &!!)',##! #,##! !#!/! )/&-,&&! (' + D 1 +# D ++ D 1 sin D çözüm kavrama sorusu +?;C 1 +# ?;q + ?;q !13 1 1 2 < Cevap: 2 çözüm kavrama sorusu ++<>;C ++ <>;q !13 1 <>;q 1 :35;q ?;q= 1 ?;q 1 3 2 2 3 2 3 2 Cevap: çözüm kavrama sorusu 2 3 3 A'++A A'++ A 13 A 1 ' +# A A 1 +# A + A Cevap: secx çözüm kavrama sorusu +# A ++ A +# A ++ A #13 +# A A 1 A +# A A ' 1 A +# A Cevap: cosx 78 Trigonometri - 1 soru 1 soru 5 +2;C +#A'+A ! = 2 3 3 = 3 3 ##!* E= 3 2 D= < = 1 2 =A soru 2 2 3 3 E= 3 3 D= 2 3 3 3 3 = =++A 0NO808YAYINLARI = soru 3 ! =S< =S3 E=; D=3 =+A E=+#A D=A =+#A soru 7 =3 =< soru 4 = 1 2 E=A D=+#A =A soru 8 ++ 11S ? 2 2 + 6;CS 6;C ##!* ! 1–A =++A 1 1 +2 A +# + 2 A ##!* +35;C =< D=+A A + A ##!* ! 3 2 E=A soru 6 ++3<;C = =+#A =3 2–B 1 E= 2 D=S3 3–B =S3 =S< 4–E 5–E 79 =; E=3 6–D D=A 7–A =++A 8–C Trigonometri - 1 çözüm kavrama sorusu 1 M':4;CS= + 2 ifadesi!13 1 + 2 2 sin a+ 1 1 +#2 +#2 :4;CS=L+# 2 sin a+ 1 2 M':4;CS=L +#2 '+# + 2 1 1 L3M3L< Cevap: 2 çözüm kavrama sorusu 2 3M A 3 2 A #13 3 2 A +#2 A +#2 A 2 A +#2 A 3 +#2 A + 2 A 2 Cevap: sec x çözüm kavrama sorusu :AS+A=':AM+A= A 3 ¬ A 3 ¬ ' :AS+A=':AM+A=L +# A +# A ® +# A +# A ® #13 A 3 A 3 ' +# A +# A +#2 A +#2 A 2 A 3 +#2 A 1 Cevap: –1 çözüm kavrama sorusu A ++ A +# A A ++ A +# A #13 A 3 +# A A A A 2 A 3 +#2 A 3 +# A 3 +# A 3 +# A A :3 +# A= :3 +# A= 3 +# A :3 +# A= Cevap: 1+cosx 80 Trigonometri - 1 soru 1 soru 5 1 1 + 2 A 1 1 3 2 A 3 +# 2 A ifad##!* 2 = A 2 =++ A 2 E=+ A ifad##!* 2 D= A 2 =3 =+# A soru 2 E=3 D=+#A 2 =A =++ A 0NO808YAYINLARI =+#A soru 3 2 3M+# A 2 2 =++ A 2 E=+ A D= A 2 2 E= A 2 D=S A 2 =S+# A 2 2 :3S+ A='+# A =A =+# A =< E=3 D=S3 =S< soru 8 3 2 A 3 +#2 A 3 ++ 2 A 3 + 2 A ifad##!* 3 2 A 3 +# 2 A ifad##!* 1–D 2 =+# A ##!* soru 4 2 2 =+# A soru 7 ##!* = A D=<+#A 3 +# 2 A 3 2 A ifad##!* ifad##!* =3 E=<A soru 6 A +# A ++ A + A =A =< 2 =+# A 2–C 2 2 E=+ A D=++ A 3–B 2 =< = A 4–A 5–A 81 =3 E=S3 6–E D=<A 7–D =<+#A 8–C Trigonometri - 1 çözüm kavrama sorusu A 3 +# A 3 +# A A A 3 +# A 3 +# A A A:3 +# A= 3 +# A A 3 +#2 A :3 +# A= A :3 +# A= #13 2 A 2 A 3 +# A A 3 +# A 3 +# A A < ++ A Cevap: 2cscx çözüm kavrama sorusu 3 2 A ¬ 2 A 2 2 + A A A +# A +# A ® +#2 A +#2 A 2 2 3 A +# A 2 A 2 A 2 2 +# A +# A +#2 A +#2 A 2 2 3 A +# A 1 +#2 A +#2 A + 2 A 2 A 2 A +#2 A 2 #13 2 2 Cevap: 1 çözüm kavrama sorusu 1 4 A +#4 A :2 A +#2 A=':2 A +#2 A= 3 < +#2 A 3 < +#2 A 2 2 2 A +# A 3 +# A +#2 A 3 < +#2 A 3 < +#2 A 2 3 < +# A 1 3 < +#2 A 4 A +#4 A 3 < +#2 A #13 Cevap: 1 çözüm kavrama sorusu :+# A A=2 +# A < A :+# A A=2 +#2 A < +# A' A 2 A +# A +# A < A < A 1 +#2 A 2 A < +# A' A +# A < A 3 < +# A' A +# A < A 3 < +# A' A < A'+# A 1 < A < A #13 Cevap: 82 1 2sinx Trigonometri - 1 soru 1 soru 5 2 A +#2 A 3 +# A 3 A ++ 2 D ifad##!* =+#ASA =+#AMA 1 2 D ifad##!* E=AS+#A =D =+#D E=3 D=+D =++D D=<A=<+#A soru 2 soru 6 2 2 +# A 3 A 3 + 2 A 3 ++ 2 A 3 4 A +#4 A < 2 A 3 ifad##!* ifad##!* =3 E=S3 D=S< =S+#A =A =+#A E=A D=3 =S3 0NO808YAYINLARI =< soru 3 soru 7 : D +# D =2 < +# D sin D 2 sinT+# TST ##!* 3 =S T 3 = T 2 E= T 2 D=S T ifad##!* =T+#T =+D soru 4 D=+#D =3 +#4 A < +#2 A 3 3 +#2 A 1 sin D D'+# D ifad##!* 1–A E=D soru 8 2 =+#D =++D =D 2–C E=3 2 D=+# D 3–A ifad##!* 2 = D =A 4–D 5–C 83 2 = A 2 E=+# A 6–D 2 D=+ A 7–B 2 =++ A 8–B Trigonometri - 1 çözüm kavrama sorusu 1 +# A A 2 A 3 +# A < A A +# A < 3 AL<& ' #!&/-* %913 ñ5 2 +# A 1 6 x B Cevap: 1 5 çözüm kavrama sorusu D +# D D +# D C 1 D +# D D +# D 3 2 #!&/-* % tanD13 3 2 3sinDM2+#DLDS+#D 2sinDLS>+#D sin D +# D 4 < DLS<& ' Cevap: –2 çözüm kavrama sorusu 6AL S 2 #!&/-* % <A +# 2A ½ ¾ 2A <A 2A +# <A ¿ %93:9 #13 :93%9 <A' 2A +# 2A'+# <A 6A S < <A' 2A s<A' 2A 1 Cevap: 1 çözüm kavrama sorusu ?ALS AM6ALS 93,9 #!&/-* % #13 >93%9 6ALSSA 6AL:SSA= 6ALA& ' >AM<ALS >ALSS<A >AL:SS<A= >ALS<A& ' A' >A 6A'<A A': <A = si A' 2A 1 Cevap: –1 84 Trigonometri - 1 soru 1 soru 5 6 +# A 3< A #!&/-* %9 = 6 3< = 6 32 S 2 >A #!&/ -* % E= 3< 32 D= 32 3< = * 3< 6 =2 soru 2 =< 6 6 = E= < < D= 3 < = < * 0NO808YAYINLARI =< soru 3 A +# A < A +# A < 2 #!&/-* %9 = 1 6 E= 6AL D= 1 6 D=S3 =S< S 2 #!&/ -* % 1 2 1 E= 2 =3 soru 7 93:9 # #!,93%9 * = 6 =S< soru 4 =S3 E=3 1 D= 2 =< soru 8 6 +# A A 3 +# A A < #!&/-* %9 = 2 =S< QQ S ,9 3%9 ##! :S ¬ ,93 \ J9 % ® #!&/-* % = 6 D=S3 S 2 5A #!&/-* %9 6 E=3 soru 6 AS<+#AL; = :93%9 # #!%939 1 = 3 PALSS2A 1 D= 3 E= 3 #!&/-* % >93:93%9 ##!S ¬ S >9 % ® = 2 * = 1–A 2–E 3–E 4–B 1 2 5–C 85 = 3 E= ; 6–D D= 3 7–C = 1 2 8–D Trigonometri - 1 Trigonometrik Fonksiyonların Periyotları: f:A o!) ,###!'A#!( %,:AM0=L,:A=)!//!$#(, 0 ! ,,##$ #&,##%0,##$ #&& ' %N%:z;=#!( % n:A = ½° S 2S %., & ' ¾ ,##! $ #& |a | |a | -:A= +#n:A =°¿ ,:A= n:A = ½° S & ' ¾ fonksiyonlar$ #& |a | -:A= +#n:A =°¿ ,:A= çözüm kavrama sorusu 2 2 ,:A=L :2AM3= ,:A=L :2AM3=,##$ #&.,#!&/&% 6 -:A=L2+# :>A= 0013 0 S |3| S ' 3 6 -:A=L2+# :>A=,##$ #&#!&/&% 0 2S |4| 2S 4 S & ' 2 Cevap: 3 ,:A=L<' :AS3= -:A=L+# :S6AM<= % 3 2 çözüm kavrama sorusu S S 3 ,:A=L<' :AS3=,##$ #&% ? 0 0013 S |1| S ? -:A=L+# :S6AM<=,##$ #&% 0 S I 6I S 6 Cevap: S % S 5 çözüm kavrama sorusu P 3sin :<AM3=,##$ #&% >A 3¬ PA 3¬ ,:A= 2 P <'+# < 3 ® 2 ® 0 0013 2S 4 3 2S 4 3 3S 2 2 PA 3¬ ,##$ #&% <+# 2 ® 0#$! & & -## ,##! $ #&! !$%$ #&! #! ,##$ #&! ' Q Q 2Q P P P 2 2 2Q <Q ¬ #:2Q%<Q= ?Q ?Q # % < P ® #:<%P= 3 0 ?S,##$ #&& ' Cevap: 6S 86 Trigonometri - 1 soru 1 soru 5 A ¬ ,:A= 4 6 2 ® 2 ,:A=L+# A 00#!* = S 4 = S 2 E= S D= 3S 2 fonk00#!* = <S = soru 2 S 4 00#!* S < E= S 2 D= S ? = S 3< = 0NO808YAYINLARI = 5S 2 00#!* = S E= S < D= S > = >S 2 E= <S 2 D= S 2 = S ? A ¬ A ¬ ,:A= P 3 +#> 3; < ® 6 ® 3 fonk00#!* = S 5 =<S soru 4 =6S E=3;S D=36S =<;S soru 8 >A ¬ A ¬ ,:A= +#? P P 2 6 2 ® ® 2A 6 ¬ ,:A= +#4 2 ® fonk00#!* 1–C = <S soru 7 ,:A=L :<AM33= 4S 2 3S 2 D= fonk00#!* soru 3 = E= S 2A ¬ ,:A= +# 6 6 4 ® 4 = <S S 2 soru 6 ,:A=L :?AM3= = S = = S 2 –D E= S 2 D= 3–B S ? = fonk00#!* S 3< =<6S 4–A 5–E 87 =36S E=3;S 6–B D=6S 7–E =2S 8–B Trigonometri - 1 Trigonometrik Fonksiyonların Grafikleri: 0 -## ,##! - ,! .(! *+,##$ #&! 'X #& !/&- ,.(! &/ $ #& !! &- , &! ' y y 1 O 1 p 2 3p p 2 1 y=sinx 2p x O p 2 1 y=cosx x 2p çözüm kavrama sorusu 3p p 2 ,:A=L<A ,:A=L<A,##$ #&0L<S& ' 0!113 x sinx f(x)=2sinx 0 0 0 p 2 1 2 p 0 0 3p 2 1 2 2p 0 0 y 2 1 p 2 1 2 f(x)=2sinx 2p x çözüm kavrama sorusu 3p p 2 ,:A=L2+#:<A= ,:A=L2+#:<A=,##$ #&0LS& ' 0!113 x cos2x f(x)=3cos2x 0 1 3 p 4 0 0 p 2 1 3 3p 4 0 0 p 1 3 y 3 2 1 p 1 4 2 3 88 p 3p 2 4 f(x)=3cos2x p x Trigonometri - 1 soru 1 soru 3 ,:A= A 2 ,:A=L2+#<A fonksi0!#!* 0!#!* A) y A) y B) y C) y B) y 3 2 2 2 1 O p 2 O x p 2 1 1 3p p 2 2p 1 3p p 2 2p p 2 1 1 2 O x 1 2 O 3p p 2 2p p 2 1 x p 4 2 p 4 1 O 3p p x 1 4 E) y 3 E) y 2 1 O 1 1 3p 2p x 2 O p 2 3p p 2 p 4 p 3p 2 4 p 3p 4 p 1 x O 1 p p 4 2 x 2 3 0NO808YAYINLARI p 2 p 3p p x 4 2 2 1 2 O 1 2 p 4 p 2 3 D) y D) y 2p x 1 2 soru 2 soru 4 y y 1 O 1 p p 8 4 3p p 8 2 2 1 O 1 2 x =<A E=<A D=>A p 2p 3p 4p x 4!/0#!* 4!/0#!* =>A p 2 1 O 3p p x 1 4 2 =<>A = +# 1–C C) y 2–D A 2 = < +# 3–A 89 A 2 E= +# A 2 D= < +# A = < +# <A 4–B Trigonometri - 1 çözüm kavrama sorusu ,:A= 2 A 2 ,:A= 2 A ,##$ #&0L<S& ' 2 p x p 2 x tan Tanýmsýz 1 2 0!113 x 3tan Tanýmsýz 3 2 0 p 2 p 0 1 Tanýmsýz 0 3 Tanýmsýz y p p 2 p 2 O 1 2 3 x p çözüm kavrama sorusu 3 2 1 ,:A=LS+#<A ,:A=LS+#<A,##$ #& 0 0!113 S & ' 2 p 4 0 p 4 p 2 cot2x Tanýmsýz 0 Tanýmsýz 0 Tanýmsýz cot2x Tanýmsýz 0 Tanýmsýz 0 Tanýmsýz x p 2 y p 2 p 4 O 90 p 4 p 2 x Trigonometri - 1 soru 1 soru 3 0!#!* A 4 0!#!* A) A) y ,:A= ,:A=L<A p 2 B) y p 4 2 p 4 2 p 2 p x 2 D) p 1 4 p 14 p p 2 4 1 p x 2 E) p 4 p 2 B) y 1 O 1 x p 2 3p p 2 C)y p 2 1 2p x O 1 p D)y y 1 2p 3p 2 x O 1 3p 4p p 2p x E) y 2 p 4 p 2 p 4 x p 4 O x p 2p 3p 4p 1 p 2p x O 1 3p 4p x 2 0NO808YAYINLARI p p 2 4 2 y 1 y 2 C) y +# soru 2 soru 4 y y 1 p O p 8 4 1 p 8 p 4 x p 1–A =A E=SA D=S A 2 p O 4 1 1 p 4 p 2 p x 4!/0#!* 4!/0#!* =<A p 2 = +# <A =S<A 2–E = +# A 3–C 91 E= +# A 2 D= +# A = +# A 2 4–B Trigonometri - 1 Trigonometrik Fonksiyonların Tersi (Ters Trigonometrik Fonksiyonlar) sin D 1 &!.*(:;C%2?;C= !/&DL2;CDL36;C& ',##)!-* % 2 R sin R R 30° sin 30° 1 2 R 1 2 ,## ! ) ! /!(' 150° 150° S3 sin % ,## #! sin1 @##! #!!. * #!! - '0 -## ,##! * #!&/&% ! #!!! .-&/ ! .! ' Kosinüs Fonksiyonunun Tersi (Arccos) # ,## * #! . &/ ! )/& - ! +# ,## S3 +# L ++##! ,&&! ' p 2 +#J;%S] oJS3%3K#!( % y ++#JS3%3KoJ;%S] L ++#AAL+# p 0 x 3p 2 çözüm kavrama sorusu 1¬ ++# 2 ® 1 1¬ 1 ++# LA L+#A& '+#AL AL?;C 2 ® 2 2 AL22;C& %+ ++#,##&/ !13 ;CdAd35;C#!&/&AL?;C& ' Cevap: 60° çözüm kavrama sorusu 3 ¬ ++# 2 ® 3 ¬ 3 3 ++# L+#A& '+#AL LA 2 ® 2 2 AL36;CAL<3;C+%36;CJ;C%35;CK#!&/& !13 AL36;C& ' Cevap: 150° 92 Trigonometri - 1 soru 1 soru 5 1¬ ++# 2 ® 3 ¬ ++# 2 ® ! ! =2;C =>6C E=?;C D=4;C = =3<;C soru 2 S 2 S < E= 2S > D= <S 2 = 6S ? = 0NO808YAYINLARI = ++#:;= = S ? E= S 2 D= S < = 3S < 1–A = S < = S 2 E= 2S 4 D= S = 6S 4 soru 7 ++#:S3=M +#:3= = S ? = S > E= S 2 D= S < = S soru 8 1¬ 1¬ ++# ++# 2 ® 2 ® ++#:S3= ! = ;q S > soru 4 S 4 ! = ;q D= ! soru 3 S ? E= 2 ¬ ++#:3= ++# 2 ® ! S > 2S 2 soru 6 2 ¬ ++# 2 ® = = = S 2 2 –C ! E= S D= 3–D 3S 2 =;C = <S 4–C 5–B 93 =4;C E=3<;C 6–A D=36;C 7–E =35;C 8–E Trigonometri - 1 Sinüs Fonksiyonunun Tersi (Arcsin) ,## * #!.&/ ! )/&-! ,## S3 sin L +#! ,&&! ' p 2 y ª S Sº sin: « % » oJS3%3K#!( % ¬ 2 2¼ 0 x ª S Sº +JS3%3Ko « % » ¬ 2 2¼ L +AAL p 2 çözüm kavrama sorusu 3 ¬ + 2 ® 3 3 ¬ LA& ' + LA 2 ® 2 !13 AL 3 AL?;CAL3<;C& %+ 2 ª S Sº + ,## &/ « % » #!&/& ¬ 2 2¼ AL?;C& ' Cevap: 60° çözüm kavrama sorusu 1¬ + 2 ® 1¬ 1 + LA LA& ' 2® 2 !13 AL 1 AL<3;CALS2;C& ' 2 ª S Sº + ,## &/ « % » #!&/& ¬ 2 2¼ ALS2;C& ' Cevap: – 30° çözüm kavrama sorusu 1¬ +# + 2® 1¬ +# + 2 ® A !13 1 1 + A A 2 2 AL S 1 old/-* AL & ' ? 2 Q 1¬ 3 +# + +# & ' <® ? < Cevap: 94 3 2 Trigonometri - 1 soru 1 soru 5 1¬ + 2 ® ! ! =4;C =P6C E=?;C D=>6C =2;C = soru 2 3 2 S 4 E= ; D= S 2 = S 4 = 0NO808YAYINLARI = 2 ¬ + 2 ® = S 3 E= S 2 D= S 2 = 1–E 2 2 = 3 2 = 3 2 E= 3 2 D= 2 2 = 1 2 = S 5 soru 7 1¬ 1¬ + + 2 ® 2 ® = E= S < D= S > 3 ¬ 3 ¬ ++# +# + 2 ® 2 ® +:S3=M +:;= S 5 D= soru 8 ! = 2 2 = ; S 4 soru 4 1 2 ! S 4 E= ! soru 3 = 1 2 1¬¬ + 2 ®® ! S 2 = soru 6 +:3= = 3 ¬ +# + 2 ® = S > 2–D E= S < 3–A D= ; = S > =<2 4–C 5–B 95 =2 E=< 6–E D=3 7– A = 1 2 8– D Trigonometri - 1 Tanjant Fonksiyonunun Tersi (Arctan) ve Kotanjant Fonksiyonunun Tersi (Arccot) 0U,## { +{& ' Q Q¬ tan: , o#!( % 2 2 ® #U,## { ++#{& ' cot: (0,S) o R Q Q¬ Arctan: R o , 2 2 ® y=Arctanx x=tany Arccot: R o (0,S) y=Arccotx x=coty p 2 y y 0 p x x p 2 çözüm kavrama sorusu Arctan(1) Arctan(1)=x ise 1=tanx Q Q¬ tanx=1 ve x , #!&/-* % x 2 2 ® !13 S & ' 4 Cevap: S 4 çözüm kavrama sorusu Ar++#:S3) ++#:S2=LAS3=cotx !13 +#ALS3 ve x(0,S=#!&/-* %AL36;C& ' Cevap: 150° çözüm kavrama sorusu sin(Arctan(1)) sin( Arctan(1)) !13 x diyelim, Arctan(1)=x ise 1=tanx Q Q¬ tanx=1 ve x , #!&/-* % x 2 2 ® sin(Arctan(1))=sin S 4 S ' 4 2 2 Cevap: 96 2 2 Trigonometri - 1 soru 1 soru 5 +:2= ! ! = 2S 2 = +#: +:3== S < E= S 2 D= S > = S ? = soru 2 3 2 S > E= S 2 D= S 2 = S ? = 0NO808YAYINLARI = 3 2 = S 2 E= S > D= S ? = 2S 2 = 3 2 E= 3 D= 1 2 = 3 2 = 1 2 E= 3 D= 3 2 = 1 2 sin: +:3== ! ifa! 1–C 1 2 soru 8 1 ¬¬ ++# 3 ®® 2 = ! soru 4 = = ; sin: ++#:2== ! S < D= 3 soru 7 ++#:3= = 1 2 ! soru 3 E= 1 ¬¬ +# ++# ®® 3 ! S ? 2 2 soru 6 1 ¬ + 3 ® = = = 1 3 2–A E= 3 D= 3–C 1 3 = 3 2 = 4–A 2 2 5–B 97 = 1 2 E= 6–B 1 2 D= 2 2 7–E = 3 2 8–A Trigonometri - 1 çözüm kavrama sorusu Q ¬¬ Q ¬¬ Arccos cos ve Arccos cos 4 ®® 4 ®® 2 ¬ Q ¬¬ Arccos cos Arccos 2 ® 4 ®® 2 2 !13 ¬ 2 Arccos 2 =x ise cosx= 2 2 ® S x[0,S]#!&/& x 4 2 ¬ Q ¬¬ Arccos cos Arccos 4 ®® 2 ® 2 2 2 ¬ =y ise y= S ! ' Arccos 2 ® 4 Q ¬¬ Q ¬¬ Arccos cos ile Arccos cos 4 ®® 4 ®® ,&! #+#!&/&&(' S S Cevap: 4 , 4 çözüm kavrama sorusu 3 ¬¬ + 4 ®® A 5 !13 3 ¬¬ + A 4 ®® x diyelim 3 3¬ 3 + LAAL 4 ® 4 x B 4 &.-&AL 3 ! ' 5 Cevap: 3 5 çözüm kavrama sorusu C : +A= A #13 : + A= y diyelim 1 x +ALLA 2 2 |BC| =|AB| SIEI 2 2 L3SA y B L 98 óõ1xõ2 x 1 x2 C |BC|=3SA 2 ! ' Cevap: x 1 x2 Trigonometri - 1 soru 1 soru 5 Q ¬¬ + ? ®® 3¬ +# + 6® ! = 2S 2 = S 2 ifa##!* E= S ? D= S ? = S 2 = soru 2 6 > = S ? E= 2S 2 D= S 2 = S ? = 0NO808YAYINLARI = 6Q ¬¬ ++# +# 3 ®® ! S 3 = <S 3 6 < = E= 6S 3 D= S 3 = 6S 3 2 > 6 E= 6 6 D= < 6 6 = 2 6 6 +#: ++#A= = 3 A2 A = A 3 A2 E= 3 A 2 D= A = 3 A soru 8 1¬ + A® ifa##!* = 3< 32 E= 6 3< D= 3< 6 ifa##!* = 32 3< = 3 3 A 2 2–A 3–A 4–B 5–D 99 = 3 A 2 D= 1–C = soru 7 6¬ +# + 13 ® 6 32 > 2 ifa##!* soru 4 = D= ifa##!* soru 3 = > 6 : +<= ! S 2 E= soru 6 Q ¬¬ + 3 ®® = 2 6 A 3 A2 6–D E= = 3 A2 A A 3 A2 7–B 8–A Trigonometri - 1 çözüm kavrama sorusu +AL A #!&/-* %#13 +ALAL& ' L 1 A 3 A2 & ' x a B C óõ1xõ2 x Cevap: çözüm kavrama sorusu +: A= 1 - x2 S ? A ñ5 #!&/-* %913 x B +:A=L 1 AL C 2 S ? AL +#AL S ? 1 2 2 6 Cevap: 2 5 çözüm kavrama sorusu 4¬ +# Q + 6® 4¬ +# Q + L+#:SSA=LS+#AL 6 A &! ® !13 + 4 4 LAAL 6 6 A 5 4 +# A 3 6 4¬ 3 +# Q + +# A 6® 6 x B C Cevap: 3 5 çözüm kavrama sorusu 3 +:AS2= ª S Sº +JS3%3Ko « % » #!&/&% ¬ 2 2¼ +,##JS3%3K& ' 0#$13 S3dAS2d1 2dAd>! ' 100 Trigonometri - 1 soru 1 soru 5 5¬ Q ++# 3P ® ++#AL #!&/-* %! = 3 3 A2 = D= A ifa! E= 3 A 2 3 A2 3 A2 A = 36 3P 5 3P D= 5 36 = 36 3P Q ¬ +# +< 2 ® #!&/-* %!#!* 3 A2 A = D= A 3 A2 E= 3 3 A 2 3 = A ifa! = 0NO808YAYINLARI = 3 A 2 soru 3 < 6 6 = 6 6 E= 6 6 D= < 6 6 = > 6 6 soru 7 S +:+# A= 4 #!&/-* %9 2 = 1 3 +:<AM3= 0 # $ #! * E= 3 D= 1 2 = < =JS3%;K soru 4 =JS3%3K E=J;%3K D=J3%;K =J3%<K soru 8 ++#: A= A P ¬ ++# 2 ® S 3 #!&/-* %9 1–C E= soru 6 +AL = < 5 36 3 A2 A = soru 2 = = = 1 2 E= 2–E 0 # $ #! * 1 6 D= 3–C 2 6 = 6 =J>%PK 4–A 5–E 101 =J>%4K E=J6%4K 6–D D=J6%3;K 7–A =JP%4K 8–C Trigonometri - 1 Kosinüs Teoremi .-& (!/ ! &.*!.!&/&.+ (!/!. (!! ! .-.! -## # ! !.## !! ('1# .(*! !:*! !=.*((# !&/(# ! &## (#!!/! ' A IIL+ %IEIL IEIL #!( % 2 2 2 2 2 2 2 2 2 a L M+ S<'+'+#A c b L M+ S<'+'+# b + L +b S<''+#E a B C çözüm kavrama sorusu A 60° E.- ## &% :E=L?;C A L< +3 S<'<'2'+#?;C 1 2 A L>M4 2 '<'2' 2 2 A L32S? 2 IIL< 3 2 IEIL2 IEILA x C 2 2 A LP #!&/-* % B 2 ALP 9 Cevap: 7 br çözüm kavrama sorusu A ## &% 2 2 2 6 L> MP S<'>'P'+# <6L3?M>4S6?'+# 5 4 <6L?6S6?'+# S>;LS6?'+# B C 7 +osL E.-%IIL> %IEIL6 %IEILP >; 6? 6 P Cevap: #!&/-* % çözüm kavrama sorusu A D.-&% A 2 2 II LIDI MIDI 7 4 3 E 2 C B 2 E.-%JKAJDK%IDILP %IDIL2 %IEIL< % 2 2 2 II L<6 IIL6 D&.-&+#L D 4 2 II L2 +4 x D 3 2 7 x B 5 7 2 E.-&# E 2 C 5 3 6 # &% 2 A L3; MP S<'3;'P'+# 3 2 A L3;;M>4S<'3;'P' 6 2 A L3>4S5>L?6 IDIL> %IEILA#!&/-* %9 AL?6 Cevap: 65 102 Trigonometri - 1 soru 1 soru 5 A E.- 30° :E=L2;C 4 A 2ñ3 IIL> 12 B IEIL<3 br IEILA =2< x B #!&/-* %9 =2 13 5 E=<2 soru 2 E.-%IIL6 %IEIL3< %IEIL32 C D=< C #!&/-* % =2 = 6 2< = > <4 E= 2 <2 soru 6 A E.- D= 6 3P A E.- 4ñ2 :E=L>6C x 6 4 IIL> IIL>2 br = ; IEIL? IEIL? IEIL6 45° 6 C D=>< =62 B IEILA #!&/-* % B 5 C 6 ? = =6 =<6 E=2< soru 3 A E.- x :E=L3<;C 4 IEIL> IEIL2 IILA =22 soru 4 < 2 = 2 > E= > 6 D= soru 7 A E.- x 6 JGKAJEK IGIL5 C IGEIL> B 8 H E=? D=26 =2P =>2 =P E=6< D=<32 soru 8 A 6 =66 A x E.- 3 JDKAJDK B C 8 B IEIL2 E.-%IIL2 %IEIL? %IEIL5 IEIL? #!&/-* % IEDIL3 C 6 = 3P 2? E= 36 2> D= 32 2; = E IILA #!&/-* %9 33 2; =<6 1–D 2–B 3–E 1 D 2ñ2 IDIL<2 br 34 2? C 4 IEILA #!&/-* %9 3 = ? P IGIL? #!&/-* %9 =2; = 120° 3 B 0NO808YAYINLARI #!&/-* %9 4–A 5–E 103 =<? E=<P 6–B D=2; 7–D =33 8–E Trigonometri - 1 çözüm kavrama sorusu E 4 A x 1 5 C 3 4 A 1 x !!' 5 C 3 2 B 2 2 <6L3?M>S3?'+#E B 6LS3?'+#E D %E%%E%D&#/ !%IEIL3 %IEIL2 6 !&/(&/ E.-&-!3? +/(## & (!' +#EL IEIL> %IEDIL< %IDIL6 %IILA #!&/-* %9 2 2 2 A L3 +3 S<'3'2'+#E ¬ 3 6 A 2L3; ? ' 3? 5 ® A 2L3;M 36 5 A 2L 46 5 AL 46 5 Cevap: 95 8 çözüm kavrama sorusu E.- (!! %+& ' 2 2 6 L> +2 S<'>'<'+#E 2 D 2 E ED .-& # # -!$ +#E &/ A ## &% 2 a L M+ S+ 2 2 2 2 2 2 2 2 2 a L M+ S<''+'+#(! ' #!&/-* % c a L M+ S+ b a L M+ S<'+'+#A )!! )!!' a B C l 2 + 2 <'+'+# l + < + '+# 1 l +# & ' 2 b2 + 2 + Cevap: 1 2 çözüm kavrama sorusu A ## &+#:E=L?;C!!% 2 2 2 A L> M? S<'>'?'+#?;C 4 2 x A L3?M2?S 2 '>'?' 2 1 2 A L6<S<> 2 A L<5 B 6 C AL<P E.-%IIL> %IEIL? %:E=R?;C :E=R?;C#!&/&AR<P#!!& ' #!&/ -* % 1! ! ! !13 F.-)(!/&?S>RA<RA& '<RAR<P& ' Cevap: 2<x<27 104 Trigonometri - 1 soru 1 soru 5 A x 4 E.-& (!! %+& ' 8 B 2 D 2 C 2 #!&/-* % 3 4 2 a L M+ M+ E = %E%D%E%&#/ !%IEILIEIL> %IEIL5 3 2 1 2 = 2 2 E= D= 1 2 3 2 = IEDIL< %IDIL2 %IILA #!&/-* %9 => E=6 D=? =5 soru 6 A 1 D soru 2 E.- IDIL3 4 3 IDIL2 IIL< 2 2 E C 5 IDIL> IEILA#!&/-* %9 =?4 =P; E=?< soru 3 D=62 A D x 5 6 IIL? =P4 8 ED&&* - E IDIL5 B C = S ? S > E= S 2 D= S < = 2S 2 A soru 7 E.- 3 IIL2 2 =6 E=? #!&/-* % D=<3; x B C 9!!$#!* =>3 =:3%<= soru 4 IIL? 180°a 6 4 IDIL5 8 IDEIL2 C =63; 2–E 3–B A 10 6 :E=^3<;C 3 a x B C #!&/-* %9!!$#!* =:3>%3?= D=632 =:3%3;= IEIL3; #!&/-* %9 6 3; E= 2 D=:3%2= IIL? D IEILA E=:3%P= E.- x B IEIL> =:3%6= soru 8 A :=M:D=L35;C 1–D = :E=R?;C IILA #!&/-* %9 =3; 2 IEIL< IDIL6 => 2 a L M+ S2+ #!&/-* %#!* B IEIL6 E.-& (!! %+& ' x 0NO808YAYINLARI =2 =:3>%3P= E=:3>%35= D=:>%3>= =:>%3?= =636 4–C 5–B 105 6–A 7–C 8–A Trigonometri - 1 Sinüs Teoremi A F.-! & - (!/%# -* . .# .-. !. .$) ' IIL+ ' b c l IEIL ' + l E 2R IEIL ' a B C çözüm kavrama sorusu A a 4$ O l sin A 5 2;q / R 8 l IEIL5 30° B :E=L2;C 013 C + l E 2R 5 1 2 2R 2R Cevap: 8 <L3?L5 çözüm kavrama sorusu A l + l E 2R # &% 4 2ñ3 60° 4 a B 3 C 4 ?;q 2 3 >'DL<2'?;C D >' D < 2' sin D a ñ7 E.-%IIL<2 %IEIL> %:E=L?;C +# D :E=LD#!&/-* %D13 3 2 3 4 P 4 Cevap: 7 4 çözüm kavrama sorusu A 30° A 30° a 6 4 D <IDEIL2IDI IDEIL2IDIL< a B C 2k :ED=L35;CST sinD13 C 3k 4 2k 1 T 2 DE.-. :DE=LD%<IDEIL2IDI#!&/-* % D.-. 180°q D 2k 2;q E.-%IIL> %IEIL? %:D=L2;C :D=LT 6 4 q B 2R # &% 4 sin T T 1 2 3k sin D sin D 106 ? 2 :35;q T= D 1 k' 1 k sin D 2 2 ? sin D T ' T < Cevap: 1 2 Trigonometri - 1 soru 1 soru 5 A A 60° 4$ /0 R 12 O B 4 120° C 4 a B C E.-%IIL> %IEIL3< %:E=L3<;C < 2 = = 2 < 2 E= < 2 3 D= > 2 3 = :E=LD#!&/-* % sinD 5 2 3 = = E= 2 < D= < 2 2 = ? ? A 4$ 6ñ2 / 8 120° 45° B 45° B =? C E=4 D=3< soru 3 =35 A &E.- x . !. .$2 30° B C E.-%IEIL5 %:E=L3<;C%:E=L>6C #!&/-* % 0NO808YAYINLARI =2 2 2 soru 6 A soru 2 2 ? =>2 =>2 E=? D=<? =>? soru 7 A 10ñ2 C #!&/-* % 45° 30° U9 B C E.-%IEIL3;< %:E=L2;C%:E=L>6C =3 =< E=2 D=> =? #!&/-* % =3< soru 4 E=<; soru 8 A 5 q 4 3 IEIL> C :D=LD B D C E.-%IIL? %IEIL6 %:E=L2;C%:E=LT :DE=L?;C #!&/-* % sinT IDEIL<IDI#!&/-* %sinD = 6 ? 1–D = 6 3< 2–D E= 6 32 D= 3–C 3 3< =<6 a 60° IIL2 30° D=<> A E.- 6 B =36 = ? 32 = 4–B 2 2 5–A 107 = < 2 2 E= 6–E ? ? D= < ? 2 7–C = 2 ? > 8–A Trigonometri - 1 Trigonometrik Alan Formülleri A 0 -## &!.-!*!-! !! $!- c .#* & *! !!)!& ' 1 !:E=L ''+'A 2 b a B !:E=L 1 ''+' 2 !:E=L 1 '''E 2 C çözüm kavrama sorusu A !,# !&% 1 l !:E=L IEI'I EI'E 2 4 30° 6 B 1 '''E 2 1 '>'?' 2;q 2 1 1 '>'?' ? 2 2 2 C E.-%IEIL> %IEIL? %:E=L2;C Cevap: 6 #!&/-* %Q 13 çözüm kavrama sorusu A 45° 60° x 2IDIL<IDEIIDIL<IDEIL2 !! # ! # )#!&/&% 2ñ2 :D= :DE= B D < 3 1 'A'I DI' >6q 2 1 '< <'I DI'?; 2 C E.-%IEIL<< %:D=L>6C :DE=L?;C%2IDIL<IDEI%IILA A' #!&/-* %913 2 2 A 2 3 3 2 2' 2 A 2 3 < 3 4 3 3 Cevap: 4 3 3 çözüm kavrama sorusu A A 2 2 D D 3 3 a 6 x C B ED .-%IDIL< %IDIL2 E B 6 C x E :E=L:D= IEIL? %IEILA %:E=L:D= 1 1 I I'IEI' D 'IDI'II' D 2 2 1 1 '6'?' D '2':A ?=' D 2 2 #!&/-* %913 2;L2AM35 2AL3<AL> 108 Trigonometri - 1 soru 1 soru 5 A 60° E.- E.- 4ñ3 IIL>3 br A 2 IIL2 br IEIL< IEILA :E=L?;C :D=L?;C B #!&/-* % C ñ2 D 60° :DE=L>6C <'IDEILIDI Q 45° x B C #!&/-* %9 => =? E=5 D=3; =3< = soru 2 2 2 = 3 2 A 10 IIL3; B :E=L36;C B C D D.-%JKAJEK%IIL<2 %IDIL> E=3; D=3< =36 A soru 3 0NO808YAYINLARI =? 5 IEIL6 =3 Q" =< 8 B =52 D=3;2 soru 4 =3 =3<3 30° 45° E.- x 6ñ3 C 4 :DE=L>6C IDIL3 B =< E=2 D D C !:E=L2 D=>? 3–D =6 A 2 E 3 2 D 1B #!&/-* % IILA#!&/-* %9 E=<? D=> IEIL2 IEIL2 2–E 8 IIL< :D=L2;C =>2 x soru 8 A IDILIDEI E :E=L:D=#!&/-* %9 E=42 IEIL?3 br =2 A B #!&/-* %Q D=< 2 IEDIL> IILA C E=2 soru 7 IEIL5 120° :E=L3<;C 1–B Q #!&/-* % IIL< E.- =<2 4 C 6 #!&/-* %Q IEIL5 =<? 30° 2ñ3 150° IEIL? =6 D=<2 soru 6 A E.- =?2 E=2 Q"] 12 =2 = 6 =?? 4–E 5–B 109 E=2 6–C 3 D= 4 6 7–D C =? 8–B Trigonometri - 1 A E.-!)/&,# !! &!&!! ' c b O R B IIL+ !:E= IEIL IEIL C a ''+ 4R Y L<LMM+#!( !:E= ': =': =': += & ':G #,# != çözüm kavrama sorusu A Y L<L>M6MP <L3? 5 4 L5 ': =': =': += !:E= 7 B 5':5 P=':5 6=':5 >= C 5'3'2'> E.-%IIL> %IEIL6 %IEILP > ? 2 #!&/-* %Q 6 çözüm kavrama sorusu B 4 O (!. E.-. !. & .$L> ' & (! 8 A . !) ' 6 IIL> !:E= IEIL? 16 ò15 C IEIL5 3? IEIL br 36 ''+ 4R >'?'5 3? >' 36 2 L236 #!&/-* %Q Cevap: 315 çözüm kavrama sorusu A Y L<L2M6M? <L3> LP 6 3 !:E= ': =': =': += P':P ?=':P 6=':P 2= P'3'<'> B 5 C 2 14 IIL? %IEIL2 %IEIL6 #!&/-* % !:E= $/0 110 ''+ < 3> 4R 2'6'? 2 14 4R 2'6'? >6 >'< 3> > 3> >6 3> ' 6? Cevap: 45 14 56 Trigonometri - 1 soru 1 soru 5 A E.- % 3 4 ^1>@%@:/:; $ / IIL> IEIL2 5 B IEIL6 C =3; =3< E=32 D=3> =3? % #!&/-* %Q =< =2 E=< soru 2 D=2 =? soru 6 A E.- IIL4 IIL? 8 6 IEIL5 IEIL33 #!&/-* % =62 4 B % Q E=26 D=23; % ^1&HT$ E=26 D=<3; 10 B /0 =236 soru 3 =?6 $ C 0NO808YAYINLARI #!&/-* % =3<6 11 9 IEIL3; IEIL> =3;2 A =23; = <P 2 6 = <4 < 2 E= <4 2 > soru 7 D= 22 2 5 C = 22 < 5 A IIL5 IEIL3; IEIL? 10 8 #!&/-* % $/ 0 =2 soru 4 5 B . !) ' 3 IIL6 E=6 6 D=? C =5 soru 8 A & (! => B 5 ^1:,>$/ C 6 O =2 IEIL? =< E=> D= 6 2 =6 IEIL6 <6 % IIL #!&/-* %Q 5 =? 1–E =4 2–E E=3< D=35 3–A =<> 4–C 5–C 111 6–E 7–C 8–E