Roboguru

Perhatikan sudut-sudut berikut! a. b. c. d. e. Tentukan letak kuadran dan tanda nilai (positif atau negatif) pada setiap sudut!

Pertanyaan

Perhatikan sudut-sudut berikut!

a. begin mathsize 14px style sin space 90 degree end style

b. begin mathsize 14px style sec space 278 degree end style

c. begin mathsize 14px style cot space 128 degree end style

d. begin mathsize 14px style cosec space 320 degree end style

e. begin mathsize 14px style tan space 20 degree end style

Tentukan letak kuadran dan tanda nilai (positif atau negatif) pada setiap sudut!

Pembahasan Soal:

sudut di kuadran I adalah sudut antara 0o sampai 90o, kuadran II di antara 90o sampai 180o, kuadran III di antara 180o sampai 270o, dan kuadran IV di antara 270o sampai 360o.

Di kuadran I, semua nilai trigonometri positif,

si kuadran II, hanya sin x dan cosec x yang bernilai positif,

di kuadran II, hanya tan x dan cotan x yang bernilai posiitf,

di kuadran IV, hanya cos x dan sec x yang bernilai positif.

Jadi,

a. begin mathsize 14px style sin space 90 degree end style

   sudut 90o merupakan batas kuadran I dan II, dimana nilai sin 90o positif 1.

b. begin mathsize 14px style sec space 278 degree end style

    sudut 278o terletak di kuadran IV, dimana nilai sec 278o positif

c. begin mathsize 14px style cot space 128 degree end style

   sudut 128o terletak di kuadran II, dimana nilai cot 128o negatif

d. begin mathsize 14px style cosec space 320 degree end style

   sudut 320o terletak di kuadran IV, dimana nilai cosec 320o negatif

e. begin mathsize 14px style tan space 20 degree end style

   sudut 20o terletak di kuadran I, dimana nilai tan 20o positif.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

H. Janatu

Mahasiswa/Alumni Universitas Riau

Terakhir diupdate 30 Maret 2021

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Pertanyaan yang serupa

Hitung nilai dari: a.

Pembahasan Soal:

Ingat nilai sudut pada kuadran I semua bernilai positif dan kuadran III nilai sinus negatif:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space fraction numerator 3 straight pi over denominator 2 end fraction end cell equals cell sin space fraction numerator 3 cross times 180 degree over denominator 2 end fraction end cell row blank equals cell sin space 270 degree end cell row blank equals cell sin space open parentheses 180 plus 90 degree close parentheses end cell row blank equals cell negative sin space 90 degree end cell row blank equals cell negative 1 end cell row cell cos space straight pi over 2 end cell equals cell cos space 180 over 2 end cell row blank equals cell cos space 90 degree end cell row blank equals 0 row cell tan space straight pi over 6 end cell equals cell tan space 180 over 6 end cell row blank equals cell tan space 30 degree end cell row blank equals cell fraction numerator 1 over denominator square root of 3 end fraction end cell end table 

kemudian substitusikan:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator sin space begin display style fraction numerator 3 straight pi over denominator 2 end fraction end style plus cos space begin display style straight pi over 2 end style over denominator 2 space tan space begin display style straight pi over 6 end style end fraction end cell equals cell fraction numerator negative 1 plus 0 over denominator 2 open parentheses begin display style fraction numerator 1 over denominator square root of 3 end fraction end style close parentheses end fraction end cell row blank equals cell fraction numerator negative 1 over denominator begin display style fraction numerator 2 over denominator square root of 3 end fraction end style end fraction end cell row blank equals cell negative 1 cross times fraction numerator square root of 3 over denominator 2 end fraction end cell row blank equals cell negative 1 half square root of 3 end cell end table  

Dengan demikian nilai dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator sin space begin display style fraction numerator 3 straight pi over denominator 2 end fraction end style plus cos space begin display style straight pi over 2 end style over denominator 2 space tan space begin display style straight pi over 6 end style end fraction end cell end table adalah negative 1 half square root of 3.

Roboguru

Apa hubungannya sudut istimewa kuadran 1 dengan kuadran 2, 3, dan 4?

Pembahasan Soal:

Hubungan sudut istimewa kuadran 1 dengan sudut di kuadran 2, 3, dan 4 adalah sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 0 degree end cell equals cell sin space 180 degree equals negative sin space 180 degree equals negative sin space 360 degree end cell row cell sin space 30 degree end cell equals cell sin space 150 degree equals negative sin space 210 degree equals negative sin space 330 degree end cell row cell sin space 45 degree end cell equals cell sin space 135 degree equals negative sin space 225 degree equals negative sin space 315 degree end cell row cell sin space 60 degree end cell equals cell sin space 120 degree equals negative sin space 240 degree equals negative sin space 300 degree end cell row cell sin space 90 degree end cell equals cell negative sin space 270 degree end cell row blank blank blank row cell cos space 0 degree end cell equals cell negative cos space 180 degree equals cos space 360 degree end cell row cell cos space 30 degree end cell equals cell negative cos space 150 degree equals negative cos space 210 degree equals cos space 330 degree end cell row cell cos space 45 degree end cell equals cell negative cos space 135 degree equals negative cos space 225 degree equals cos space 315 degree end cell row cell cos space 60 degree end cell equals cell negative cos space 120 degree equals negative cos space 240 degree equals cos space 300 degree end cell row cell cos space 90 degree end cell equals cell negative cos space 90 degree space space equals negative cos space 270 degree equals cos space 270 degree end cell row blank blank blank row cell tan space 0 degree end cell equals cell negative tan space 180 degree equals tan space 180 degree equals negative tan space 360 degree end cell row cell tan space 30 degree end cell equals cell negative tan space 150 degree equals tan space 210 degree equals negative tan space 330 degree end cell row cell tan space 45 degree end cell equals cell negative tan space 135 degree equals tan space 225 degree equals negative tan space 315 degree end cell row cell tan space 60 degree end cell equals cell negative tan space 120 degree equals tan space 240 degree equals negative tan space 300 degree end cell row cell tan space 90 degree end cell equals cell negative tan space 90 degree space space equals tan space 270 degree equals negative tan space 270 degree end cell end table 

 

 

 

Roboguru

Hitung nilai dari: b.

Pembahasan Soal:

Nilai cos pada kuadran II adalah negatif sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 150 degree end cell equals cell cos space open parentheses 180 degree minus 30 degree close parentheses end cell row blank equals cell negative cos space 30 degree end cell row blank equals cell negative 1 half square root of 3 end cell end table 

Kemudian gunakna definisi cotangen dan konsep sudut negatif, ingat nilai tangen pada kuadran IV adalah negatif sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell cot space open parentheses negative 330 degree close parentheses end cell equals cell fraction numerator 1 over denominator tan space open parentheses negative 330 degree close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator negative tan space 330 degree end fraction end cell row blank equals cell fraction numerator 1 over denominator negative tan space open parentheses 360 degree minus 30 degree close parentheses end fraction end cell row blank equals cell negative fraction numerator 1 over denominator negative tan space 30 degree end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator square root of 3 over denominator 2 end fraction end style end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 3 end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction end cell row blank equals cell 2 over 3 square root of 3 end cell end table  

Kemudian substitusikan:

cos space 150 degree plus sin space 45 degree plus 1 half cot space open parentheses negative 330 degree close parentheses equals negative 1 half square root of 3 plus 1 half square root of 2 plus 1 half open parentheses 2 over 3 square root of 3 close parentheses equals negative 1 half square root of 3 plus 1 half square root of 2 plus 1 third square root of 3 equals 1 half square root of 2 plus 1 third square root of 3 minus 1 half square root of 3 equals 1 half square root of 2 minus 1 over 6 square root of 3  

Dengan demikian nilai dari begin mathsize 14px style cos space 150 degree plus sin space 45 degree plus 1 half cot open parentheses negative 330 degree close parentheses end style adalah 1 half square root of 2 minus 1 over 6 square root of 3.

Roboguru

Hitunglah hasil dari soal di bawah ini:

Pembahasan Soal:

Ingat konsep nilai pada kuadran II dan III:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space open parentheses 180 degree minus alpha close parentheses end cell equals cell negative cos space alpha end cell row cell sin space open parentheses 180 degree minus alpha close parentheses end cell equals cell sin space alpha end cell row cell tan space open parentheses 180 degree minus alpha close parentheses end cell equals cell negative tan space alpha end cell row cell cos space open parentheses 180 degree plus alpha close parentheses end cell equals cell negative cos space alpha end cell end table end style

Kemudian gunakan konsep tersebut sehingga:

 begin mathsize 14px style fraction numerator sin space 45 degree times cos space 135 degree times tan space 135 degree over denominator sin space 150 degree times cos space 225 degree end fraction equals fraction numerator sin space 45 degree times cos space open parentheses 180 degree minus 45 degree close parentheses times tan space open parentheses 180 degree minus 45 degree close parentheses over denominator sin space open parentheses 180 degree minus 30 degree close parentheses times cos space open parentheses 180 degree plus 45 degree close parentheses end fraction equals fraction numerator sin space 45 degree times open parentheses negative cos space 45 degree close parentheses times open parentheses negative tan space 45 degree close parentheses over denominator open parentheses sin space 30 degree close parentheses times open parentheses negative cos space 45 degree close parentheses end fraction equals fraction numerator begin display style 1 half end style square root of 2 times open parentheses negative 1 half square root of 2 close parentheses times open parentheses negative 1 close parentheses over denominator open parentheses begin display style 1 half end style close parentheses open parentheses negative begin display style 1 half end style square root of 2 close parentheses end fraction equals fraction numerator begin display style 1 fourth end style times 2 over denominator negative begin display style 1 fourth end style square root of 2 end fraction equals negative fraction numerator 2 over denominator square root of 2 end fraction cross times fraction numerator square root of 2 over denominator square root of 2 end fraction equals negative square root of 2 end style 

Dengan demikian nilai dari begin mathsize 14px style fraction numerator sin space 45 degree times cos space 135 degree times tan space 135 degree over denominator sin space 150 degree times cos space 225 degree end fraction end style adalah begin mathsize 14px style negative square root of 2 end style.

Roboguru

Perhatikan gambar segitiga berikut. Tentukan rusuk yang belum diketahui serta jelaskan segitiga tersebut berada dikuadran berapa jika  dan  pada sumbu .

Pembahasan Soal:

- Perhatikan increment ABC, maka:

AC equals square root of AB squared plus BC squared end root AC equals square root of open parentheses square root of 3 close parentheses squared plus 1 squared end root AC equals square root of 3 plus 1 end root AC equals square root of 4 AC equals 2 

Jika BC pada sumbu straight x, maka increment ABC berada pada Kuadran I.

- Perhatikan increment PQR, maka:

QR equals square root of PR squared minus PQ squared end root QR equals square root of open parentheses square root of 2 close parentheses squared minus 1 squared end root QR equals square root of 2 minus 1 end root QR equals square root of 1 QR equals 1 

Jika PQ pada sumbu straight x, maka increment PQR berada pada kuadran III.

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