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Pertanyaan

Tentukan nilai sinus, cosinus, dan tangen untuk sudut begin mathsize 14px style P end style dan begin mathsize 14px style R end style pada setiap segitiga siku-siku di bawah ini. Nyatakan jawaban kamu dalam bentuk paling sederhana.

a.

 

E. Dwi

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

nilai begin mathsize 14px style sin space P space dan space cos space R end style adalah begin mathsize 14px style 2 over 5 square root of 5 end style, nilai begin mathsize 14px style sin space R space dan space cos space P end style adalah begin mathsize 14px style 1 fifth square root of 5 end style, nilai begin mathsize 14px style tan space P space dan space tan space R end style berturut-turut adalah begin mathsize 14px style 2 space dan space 1 half end style

Pembahasan

Perbandingan trigonometri adalah perbandingan ukuran sisi-sisi suatu segitiga siku-siku apabila ditinjau dari salah satu sudut yang terdapat pada segitiga tersebut.

Diketahui:

begin mathsize 14px style P Q equals 4 Q R equals 8 end style 

Tentukan semua panjang sisi segitiga terlebih dahulu.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P R end cell equals cell square root of 4 squared plus 8 squared end root end cell row blank equals cell square root of 16 plus 64 end root end cell row blank equals cell square root of 80 end cell row blank equals cell 4 square root of 5 end cell end table end style 

  • Sinus

Nilai begin mathsize 14px style sin space P end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space P end cell equals cell fraction numerator Q R over denominator P R end fraction end cell row blank equals cell fraction numerator 8 over denominator 4 square root of 5 end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 5 end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 5 end fraction cross times fraction numerator square root of 5 over denominator square root of 5 end fraction end cell row blank equals cell 2 over 5 square root of 5 end cell end table end style

Nilai begin mathsize 14px style sin space R end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space R end cell equals cell fraction numerator P Q over denominator P R end fraction end cell row blank equals cell fraction numerator 4 over denominator 4 square root of 5 end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 5 end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 5 end fraction cross times fraction numerator square root of 5 over denominator square root of 5 end fraction space end cell row blank equals cell 1 fifth square root of 5 space end cell end table end style

  • Cosinus

Nilai begin mathsize 14px style cos space P end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space P end cell equals cell fraction numerator P Q over denominator P R end fraction end cell row blank equals cell fraction numerator 4 over denominator 4 square root of 5 end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 5 end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 5 end fraction cross times fraction numerator square root of 5 over denominator square root of 5 end fraction end cell row blank equals cell 1 fifth square root of 5 end cell end table end style

Nilai begin mathsize 14px style cos space R end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell cos space R end cell equals cell fraction numerator Q R over denominator P R end fraction end cell row blank equals cell fraction numerator 8 over denominator 4 square root of 5 end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 5 end fraction end cell row blank equals cell fraction numerator 2 over denominator square root of 5 end fraction cross times fraction numerator square root of 5 over denominator square root of 5 end fraction end cell row blank equals cell 2 over 5 square root of 5 end cell end table end style 

  • Tangen

Nilai begin mathsize 14px style tan space P end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan space P end cell equals cell fraction numerator Q R over denominator P Q end fraction end cell row blank equals cell 8 over 4 end cell row blank equals 2 end table end style

Nilai begin mathsize 14px style tan space R end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan space R end cell equals cell fraction numerator P Q over denominator Q R end fraction end cell row blank equals cell 4 over 8 end cell row blank equals cell 1 half end cell end table end style  

Jadi, nilai begin mathsize 14px style sin space P space dan space cos space R end style adalah begin mathsize 14px style 2 over 5 square root of 5 end style, nilai begin mathsize 14px style sin space R space dan space cos space P end style adalah begin mathsize 14px style 1 fifth square root of 5 end style, nilai begin mathsize 14px style tan space P space dan space tan space R end style berturut-turut adalah begin mathsize 14px style 2 space dan space 1 half end style

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