Roboguru
SD

a. Buktikanlah: sin 5x=14 sin5x−18 sin3x+5 sin x. (Petunjuk: 5x=3x+2x) b. Gunakan jawaban (a) untuk menghitung:  (i) 14 sin5 18∘−18 sin3 18∘+5 sin 18∘  (ii) 14 sin5 6∘−18 sin3 6∘+5 sin 6∘

Pertanyaan

a. Buktikanlah:

sin space 5 x equals 14 space sin to the power of 5 x minus 18 space sin cubed x plus 5 space sin space x.
(Petunjuk: 5 x equals 3 x plus 2 x)

b. Gunakan jawaban (a) untuk menghitung: 

(i) 14 space sin to the power of 5 space 18 degree minus 18 space sin cubed space 18 degree plus 5 space sin space 18 degree 
(ii) 14 space sin to the power of 5 space 6 degree minus sign 18 space sin cubed space 6 degree plus 5 space sin space 6 degree 

S. Yoga

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

Nilai dari 16 space sin to the power of 5 space 6 degree minus 20 space sin cubed space 6 degree plus 5 space sin space 6 degree adalah 1 half.

Pembahasan

Diasumsikan bahwa soal tersebut

a. membuktikan sin space 5 x equals 16 space sin to the power of 5 x minus 20 space sin cubed x plus 5 space sin space x.
b. (i) Nilai dari 16 space sin to the power of 5 space 18 degree minus 20 space sin cubed space 18 degree plus 5 space sin space 18 degree
    (ii) Nilai dari 16 space sin to the power of 5 space 6 degree minus 20 space sin cubed space 6 degree plus 5 space sin space 6 degree.

Ingat bahwa:

  • sin left parenthesis straight A plus straight B right parenthesis equals sin space straight A space cos space straight B plus cos space straight A space sin space straight B 
  • cos squared space straight A equals 1 minus sin squared space straight A 
  • sin space 2 straight A equals 2 space sin space straight A space cos space straight A 
  • cos space 2 straight A equals cos squared space straight A minus sin squared space straight A 

a. Membuktikan sin space 5 x equals 16 space sin to the power of 5 x minus 20 space sin cubed x plus 5 space sin space x:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 5 x end cell equals cell sin left parenthesis 3 x plus 2 x right parenthesis end cell row cell sin space 5 x end cell equals cell left parenthesis sin space 2 x space cos space x plus cos space 2 x space sin space x right parenthesis cos space 2 x end cell row blank blank cell plus left parenthesis cos space 2 x space cos space x – sin space 2 x space sin space x right parenthesis space sin space 2 x end cell row cell sin space 5 x end cell equals cell sin space 2 x space cos space 2 x space cos space x plus cos squared space 2 x space sin space x end cell row blank blank cell plus left parenthesis sin space 2 x space cos space 2 x space cos space x – sin squared space 2 x space sin space x right parenthesis end cell row cell sin space 5 x end cell equals cell 2 sin space 2 x space cos space 2 x space cos space x end cell row blank blank cell plus cos squared space 2 x space sin space x – space sin squared space 2 x space sin space x end cell row cell sin space 5 x end cell equals cell 2 left parenthesis 2 sin space x space cos space x right parenthesis left parenthesis cos squared x – sin squared x right parenthesis cos space x end cell row blank blank cell plus left parenthesis cos squared x – sin squared x right parenthesis squared sin space x – left parenthesis 2 sin space x space cos space x right parenthesis squared sin space x end cell row cell sin space 5 x end cell equals cell 4 left parenthesis sin space x space cos squared space x right parenthesis left parenthesis left square bracket 1 – sin squared x right square bracket space – sin squared x right parenthesis end cell row blank blank cell plus left parenthesis left square bracket 1 – sin squared x right square bracket – sin squared x right parenthesis squared sin space x – left parenthesis 4 sin squared space x space cos squared space x right parenthesis sin space x space end cell row cell sin space 5 x end cell equals cell 4 left parenthesis sin space x space left square bracket 1 – sin squared x right square bracket right parenthesis left parenthesis 1 – 2 sin squared x right parenthesis plus left parenthesis 1 – 2 sin squared x right parenthesis squared sin space x space – 4 sin cubed space x space left square bracket 1 – sin squared x right square bracket end cell row cell sin space 5 x end cell equals cell 4 sin space x left parenthesis 1 – sin squared x right parenthesis left parenthesis 1 – 2 sin squared x right parenthesis plus left parenthesis 1 – 4 sin squared x plus 4 sin to the power of 4 x right parenthesis sin space x end cell row blank blank cell – 4 sin cubed space x plus 4 sin to the power of 5 x end cell row cell sin space 5 x end cell equals cell left parenthesis 4 sin space x – 4 sin cubed x right parenthesis left parenthesis space 1 – 2 sin squared x right parenthesis plus sin space x – 4 sin cubed x end cell row blank blank cell plus 4 sin to the power of 5 x – 4 sin cubed space x space plus 4 sin to the power of 5 x end cell row cell sin space 5 x end cell equals cell 4 sin space x – 8 sin cubed x – 4 sin cubed x plus 8 sin to the power of 5 x end cell row blank blank cell plus sin space x – 8 sin cubed x plus 8 sin to the power of 5 x end cell row cell sin space 5 x end cell equals cell 5 sin space x minus 20 sin cubed x plus 16 sin to the power of 5 x end cell end table   

Jadi, Terbukti bahwa sin space 5 x equals 16 space sin to the power of 5 x minus 20 space sin cubed x plus 5 space sin space x.

b. (i) Mencari nilai dari 16 space sin to the power of 5 space 18 degree minus 20 space sin cubed space 18 degree plus 5 space sin space 18 degree 

Ingat bahwa sin space 5 x equals 16 space sin to the power of 5 x minus 20 space sin cubed x plus 5 space sin space x, sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell 16 space sin to the power of 5 space 18 degree minus 20 space sin cubed space 18 degree plus 5 space sin space 18 degree end cell equals cell sin space left parenthesis 5 times 18 degree right parenthesis end cell row blank equals cell sin space left parenthesis 90 degree right parenthesis end cell row blank equals 1 end table 

Jadi, Nilai dari 16 space sin to the power of 5 space 18 degree minus 20 space sin cubed space 18 degree plus 5 space sin space 18 degree adalah 1.

(ii) Mencari nilai dari 16 space sin to the power of 5 space 6 degree minus 20 space sin cubed space 6 degree plus 5 space sin space 6 degree:

Ingat bahwa sin space 5 x equals 16 space sin to the power of 5 x minus 20 space sin cubed x plus 5 space sin space x, sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell 16 space sin to the power of 5 space 6 degree minus 20 space sin cubed space 6 degree plus 5 space sin space 6 degree end cell equals cell sin space left parenthesis 5 times 6 degree right parenthesis end cell row blank equals cell sin space left parenthesis 30 degree right parenthesis end cell row blank equals cell 1 half end cell end table  

Jadi, Nilai dari 16 space sin to the power of 5 space 6 degree minus 20 space sin cubed space 6 degree plus 5 space sin space 6 degree adalah 1 half.

33

0.0 (0 rating)

Pertanyaan serupa

Buktikan bahwa: a. sin 3θ=3sin θ−4sin3 θ

18

0.0

Jawaban terverifikasi

RUANGGURU HQ

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

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia