Roboguru
SD

Himpunan penyelesaian dari persamaan sin (x+30)∘+sin (x−120)∘=0 untuk 0∘≤x≤360∘ adalah...

Pertanyaan

Himpunan penyelesaian dari persamaan sin space open parentheses x plus 30 close parentheses degree plus sin space open parentheses x minus 120 close parentheses degree equals 0 untuk 0 degree less or equal than x less or equal than 360 degree adalah...

  1. open curly brackets 45 degree comma space 135 degree close curly brackets

  2. open curly brackets 45 degree comma space 225 degree close curly brackets

  3. open curly brackets 45 degree comma space 315 degree close curly brackets

  4. open curly brackets 135 degree comma space 225 degree close curly brackets

  5. open curly brackets 135 degree comma space 315 degree close curly brackets

W. Wati

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Ingat!

sin space alpha plus sin space beta equals 2 space sin space open parentheses fraction numerator alpha plus beta over denominator 2 end fraction close parentheses times cos space open parentheses fraction numerator alpha minus beta over denominator 2 end fraction close parentheses 

dan 

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space x end cell equals cell sin space alpha end cell row cell x subscript 1 end cell equals cell alpha plus k times 360 degree end cell row cell x subscript 2 end cell equals cell open parentheses 180 minus alpha close parentheses plus k times 360 degree end cell end table 
 

Dengan menggunakan rumus trigonometri, diperoleh:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin space open parentheses x plus 30 close parentheses degree plus sin space open parentheses x minus 120 close parentheses degree end cell equals 0 row cell 2 sin open parentheses fraction numerator x plus 30 degree plus x minus 120 degree over denominator 2 end fraction close parentheses times cos open parentheses fraction numerator x plus 30 degree minus x plus 120 degree over denominator 2 end fraction close parentheses end cell equals 0 row cell 2 sin open parentheses x minus 45 close parentheses degree times cos space 75 degree end cell equals 0 row cell sin open parentheses x minus 45 close parentheses degree end cell equals 0 row cell sin open parentheses x minus 45 close parentheses degree end cell equals cell sin space 0 degree end cell end table end style

Maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 minus 45 degree end cell equals cell 0 degree plus k times 360 end cell row cell x subscript 1 end cell equals cell 45 degree plus k times 360 end cell row cell x subscript 2 minus 45 end cell equals cell open parentheses 180 degree minus 0 degree close parentheses plus k times 360 degree end cell row cell x subscript 2 end cell equals cell 180 degree plus 45 degree plus k times 360 degree end cell row cell x subscript 2 end cell equals cell 225 degree plus k times 360 end cell end table 

Untuk k equals 0, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 end cell equals cell 45 degree plus 0 times 360 degree equals 45 degree end cell row cell x subscript 2 end cell equals cell 225 degree plus 0 times 360 degree equals 225 degree end cell end table

Untuk k equals 1, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell x subscript 1 end cell equals cell 45 degree plus 1 times 360 degree equals 405 degree end cell row cell x subscript 2 end cell equals cell 225 degree plus 1 times 360 degree equals 585 degree end cell row blank blank cell text Tidak Memenuhi end text end cell end table 

Dengan demikian,

HP equals open curly brackets 45 degree comma space 225 degree close curly brackets


Oleh karena itu, jawaban yang benar adalah B.

222

5.0 (2 rating)

Pertanyaan serupa

Himpunan penyelesaian dari sin (2x−31​π)=21​ untuk 0∘≤x≤2π adalah ....

62

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