Roboguru
SD

Himpunan penyelesaian dari cos (2x−15∘)=21​2​ untuk 0∘≤x≤360∘ adalah...

Pertanyaan

Himpunan penyelesaian dari cos space open parentheses 2 x minus 15 degree close parentheses equals 1 half square root of 2 untuk 0 degree less or equal than x less or equal than 360 degree adalah...

  1. open curly brackets 30 degree comma space 165 degree comma space 210 degree comma space 345 degree close curly brackets 

  2. open curly brackets 30 degree comma space 75 degree comma space 210 degree comma space 255 degree close curly brackets 

  3. open curly brackets 30 degree comma space 165 degree comma space 240 degree comma space 330 degree close curly brackets 

  4. open curly brackets 15 degree comma space 195 degree comma space 210 degree comma space 330 degree close curly brackets 

  5. open curly brackets 15 degree comma space 150 degree comma space 195 degree comma space 330 degree close curly brackets 

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Jawaban yang benar untuk pertanyaan tersebut adalah A.

Persamaan Trigonometri Dasar

Penyelesaian persamaan trigonometri dasar bentuk cos space x equals a dilakukan dengan cara: mengubah bentuk cos space x equals a menjadi cos space x equals cos space a.

Ingat persamaan trigonometri dasar berikut:

Jika cos space x equals cos space alpha, nilai x equals alpha plus k times 360 degree atau x equals negative alpha plus k times 360 degree.

cos space open parentheses 2 x minus 15 degree close parentheses equals 1 half square root of 2 untuk 0 degree less or equal than x less or equal than 360 degree, maka diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space open parentheses 2 x minus 15 degree close parentheses end cell equals cell 1 half square root of 2 end cell row cell cos space open parentheses 2 x minus 15 degree close parentheses end cell equals cell cos space 45 degree end cell row cell 2 x minus 15 degree end cell equals cell 45 degree plus k times 360 degree end cell row cell 2 x end cell equals cell 45 degree plus 15 degree plus k times 360 degree end cell row cell 2 x end cell equals cell 60 degree plus k times 360 degree end cell row x equals cell fraction numerator up diagonal strike 2 open parentheses 30 degree plus k times 180 degree close parentheses over denominator up diagonal strike 2 end fraction end cell row blank equals cell 30 degree plus k times 180 degree end cell end table  

atau

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space open parentheses 2 x minus 15 degree close parentheses end cell equals cell 1 half square root of 2 end cell row cell cos space open parentheses 2 x minus 15 degree close parentheses end cell equals cell cos space 45 degree end cell row cell 2 x minus 15 degree end cell equals cell negative 45 degree plus k times 360 degree end cell row cell 2 x end cell equals cell negative 45 degree plus 15 degree plus k times 360 degree end cell row cell 2 x end cell equals cell negative 30 degree plus k times 360 degree end cell row x equals cell fraction numerator up diagonal strike 2 open parentheses negative 15 degree plus k times 180 degree close parentheses over denominator up diagonal strike 2 end fraction end cell row blank equals cell negative 15 degree plus k times 180 degree end cell end table  

Untuk k equals 0, maka:

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 30 degree plus 0 times 180 degree end cell row blank equals cell 30 degree end cell end table 

(Memenuhi)

atau

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell negative 15 degree plus 0 times 180 degree end cell row blank equals cell negative 15 degree end cell end table 

(Tidak Memenuhi)

Untuk k equals 1, maka:

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 30 degree plus 1 times 180 degree end cell row blank equals cell 30 degree plus 180 degree end cell row blank equals cell 210 degree end cell end table 

(Memenuhi)

atau 

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell negative 15 degree plus 1 times 180 degree end cell row blank equals cell negative 15 degree plus 180 degree end cell row blank equals cell 165 degree end cell end table 

(Memenuhi)

Untuk k equals 2, maka:

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell 30 degree plus 2 times 180 degree end cell row blank equals cell 30 degree plus 360 degree end cell row blank equals cell 390 degree end cell end table 

(Tidak Memenuhi)

atau

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell negative 15 degree plus 2 times 180 degree end cell row blank equals cell negative 15 degree plus 360 degree end cell row blank equals cell 345 degree end cell end table 

(Memenuhi)

Dengan demikian, himpunan penyelesaiannya adalah open curly brackets 30 degree comma space 165 degree comma space 210 degree comma space 345 degree close curly brackets.

Oleh karena itu, jawaban yang benar adalah A.

22

0.0 (0 rating)

Pertanyaan serupa

Himpunan penyelesaian dari persamaan cos (61​π−x)=cos (31​π−x) untuk 0≤x≤2π adalah...

164

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