RoboguruRoboguru
SD

Diketahui sin x=54​, dengan 0∘<x<90∘. Nilai cos 3x+cos x=...

Pertanyaan

Diketahui sin space x equals 4 over 5, dengan 0 degree less than x less than 90 degree. Nilai cos space 3 x plus cos space x equals...

  1. negative 18 over 25

  2. negative 80 over 125

  3. negative 42 over 125

  4. negative 6 over 25

  5. negative 12 over 25

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

  tidak ada jawaban yang tepat

Pembahasan

Ingat kembali:

cos space A plus cos space B equals 2 space cos space open parentheses fraction numerator A plus B over denominator 2 end fraction close parentheses space cos space open parentheses fraction numerator A minus B over denominator 2 end fraction close parentheses 

cos space 2 x equals 1 minus 2 sin squared x

Aturan Pythagoras:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank sisi 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 samping 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 square root of kuadrat space sisi space miring minus kuadrat space sisi space depan end root end cell end table

Perbandingan sisi pada trigonometri:

sin space x equals fraction numerator sisi space depan space sudut over denominator sisi space miring end fraction cos space x equals fraction numerator sisi space samping space sudut over denominator sisi space miring end fraction

Pertama kita tentukan terlebih dahulu cos space x:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space straight x end cell equals cell 4 over 5 end cell row cell fraction numerator sisi space depan space sudut over denominator sisi space miring end fraction end cell equals cell 4 over 5 end cell row blank rightwards arrow cell sisi space depan space sudut equals 4 end cell row blank rightwards arrow cell sisi space miring equals 5 end cell end table

Dengan menggunakan teorema Pythagoras:

table attributes columnalign right center left columnspacing 0px end attributes row cell sisi space samping end cell equals cell square root of kuadrat space sisi space miring minus kuadrat space sisi space depan end root end cell row blank equals cell square root of 5 squared minus 4 squared end root end cell row blank equals cell square root of 9 end cell row blank equals 3 end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space straight x end cell equals cell fraction numerator sisi space samping space sudut over denominator sisi space miring end fraction end cell row blank equals cell 3 over 5 end cell end table

Sehingga diperoleh perhitungan:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 3 x plus cos space x end cell equals cell 2 space cos space open parentheses fraction numerator 3 x plus x over denominator 2 end fraction close parentheses times cos space open parentheses fraction numerator 3 x minus 1 over denominator 2 end fraction close parentheses end cell row blank equals cell 2 space cos space 2 x times cos space x end cell row blank equals cell open parentheses 1 minus 2 sin squared x close parentheses times cos space x end cell row blank equals cell open parentheses 1 minus 2 open parentheses 4 over 5 close parentheses squared close parentheses times 3 over 5 end cell row blank equals cell open parentheses 1 minus 32 over 25 close parentheses times 3 over 5 end cell row blank equals cell open parentheses fraction numerator 25 minus 32 over denominator 25 end fraction close parentheses times 3 over 5 end cell row blank equals cell fraction numerator negative 7 over denominator 25 end fraction times 3 over 5 end cell row blank equals cell negative 21 over 125 end cell end table

Dengan mikian, nilai cos space 3 x plus cos space x  adalah  table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 21 over 125 end cell end table

Jadi,  tidak ada jawaban yang tepat

38

0.0 (0 rating)

Pertanyaan serupa

Misal segitiga ABC adalah segitiga sama kaki dengan AB=BC dan sin A=p. Tentukanlah: a. batas nilai  b. sin C c. cos A d. cos C e. sin B f. cos B

255

5.0

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