Roboguru

Gunakan rumus 2sinαsinβ=cos(α−β)−cos(α+β) untuk membuktikan: .

Pertanyaan

Gunakan rumus 2 sin space alpha space sin space beta equals cos space left parenthesis alpha minus beta right parenthesis minus cos space left parenthesis alpha plus beta right parenthesis untuk membuktikan: table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 54 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 18 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 fourth end cell end table.

Pembahasan:

Ingat bahwa:

  • cos space 2 a equals 1 minus 2 space sin squared a 
  • sin space a equals cos space left parenthesis 90 degree minus a right parenthesis 
  • sin space 2 a equals 2 space sin space a space cos space a 
  • 2 sin space alpha space sin space beta equals cos space left parenthesis alpha minus beta right parenthesis minus cos space left parenthesis alpha plus beta right parenthesis

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 54 degree space sin space 18 degree end cell equals cell 1 fourth end cell row cell cos space left parenthesis 90 degree minus 54 degree right parenthesis space sin space 18 degree end cell equals cell 1 fourth end cell row cell cos space 36 degree space sin space 18 degree end cell equals cell 1 fourth end cell end table 

Mencari sin space 18 degree:

Misalkan: theta equals 18 degree, maka:

 table attributes columnalign right center left columnspacing 0px end attributes row cell 5 theta end cell equals cell 90 degree end cell row cell 2 theta plus 3 theta end cell equals cell 90 degree end cell row cell 2 theta end cell equals cell 90 degree minus 3 theta end cell row cell sin 2 theta end cell equals cell sin left parenthesis 90 minus 3 theta right parenthesis equals cos 3 theta end cell row cell 2 sin theta cos theta end cell equals cell 4 cos cubed theta minus 3 cos theta end cell row cell 2 sin theta cos theta minus 4 cos cubed theta plus 3 cos theta end cell equals 0 row cell cos theta open parentheses 2 sin theta minus 4 cos squared theta plus 3 close parentheses end cell equals 0 row cell 2 sin theta minus 4 open parentheses 1 minus sin squared theta close parentheses plus 3 end cell equals 0 row cell sin theta end cell equals cell fraction numerator negative 2 plus-or-minus square root of 2 squared minus 4 cross times 4 cross times left parenthesis negative 1 right parenthesis end root over denominator 2 cross times 4 end fraction end cell row cell sin theta end cell equals cell fraction numerator negative 2 plus-or-minus square root of 20 over denominator 8 end fraction end cell row cell sin theta end cell equals cell fraction numerator square root of 5 minus 1 over denominator 4 end fraction end cell row cell sin space 18 degree end cell equals cell fraction numerator square root of 5 minus 1 over denominator 4 end fraction end cell end table 

Mencari cos space 36 degree:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 36 degree end cell equals cell cos space open parentheses 2 times 18 degree close parentheses end cell row blank equals cell 1 minus 2 sin squared 18 degree end cell row blank equals cell 1 minus 2 open parentheses fraction numerator square root of 5 minus 1 over denominator 4 end fraction close parentheses squared end cell row blank equals cell 1 minus open parentheses fraction numerator square root of 5 plus 1 minus 2 square root of 5 over denominator 8 end fraction close parentheses end cell row blank equals cell fraction numerator square root of 5 plus 1 over denominator 4 end fraction end cell end table 

Sehingga didapat:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos open parentheses 36 degree close parentheses sin open parentheses 18 degree close parentheses end cell equals cell open parentheses fraction numerator square root of 5 plus 1 over denominator 4 end fraction close parentheses open parentheses fraction numerator square root of 5 minus 1 over denominator 4 end fraction close parentheses end cell row blank equals cell fraction numerator open parentheses square root of 5 plus 1 close parentheses open parentheses square root of 5 minus 1 close parentheses over denominator 4 times thin space 4 end fraction end cell row blank equals cell fraction numerator open parentheses 1 plus square root of 5 close parentheses open parentheses square root of 5 minus 1 close parentheses over denominator 16 end fraction end cell row blank equals cell 4 over 16 end cell row blank equals cell 1 fourth end cell end table 

Jadi, terbukti bahwa table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 54 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank sin end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 18 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank degree end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 fourth end cell end table.

Jawaban terverifikasi

Dijawab oleh:

S. Yoga

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Terakhir diupdate 06 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

Pertanyaan serupa

Hitunglah tanpa menggunakan kalkulator atau tabel trigonometri: a. csc10∘+csc50∘−csc70∘

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved