Roboguru
SD

Selesaikan persamaan trigonometri di bawah ini, untuk 0∘≤x≤360∘. f. 6 sin x cos x+2sin x=1+3 cosx

Pertanyaan

Selesaikan persamaan trigonometri di bawah ini, untuk 0 degree less or equal than x less or equal than 360 degree.

f. 6 space sin space x space cos space x plus 2 sin space x equals 1 plus 3 space cos x  

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

himpunan penyelesaian dari persamaan trigonometri tersebut adalah open curly brackets 30 degree space semicolon space 109 comma 47 degree space semicolon space 150 degree space semicolon space 250 comma 53 degree close curly brackets.

Pembahasan

Ingat!

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 x equals cell alpha plus k.360 degree end cell row blank blank atau row x equals cell left parenthesis 180 minus alpha right parenthesis plus k.360 degree end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space x end cell equals cell cos space alpha end cell row x equals cell alpha plus k.360 degree end cell row blank blank atau row x equals cell negative alpha plus k.360 degree end cell end table

Maka:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell 6 space sin space x space cos space x plus 2 space sin space x end cell equals cell 1 plus 3 space cos x end cell row cell 6 space sin space x space cos space x plus 2 space sin space x minus 3 space cos space x minus 1 end cell equals 0 row cell left parenthesis 3 space cos space x plus 1 right parenthesis left parenthesis 2 space sin space x minus 1 right parenthesis end cell equals 0 end table end style  

begin mathsize 12px style cos space x equals negative 1 third space atau space sin space x equals 1 half end style    

  • cos space x equals negative 1 third 

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space x end cell equals cell negative 1 third end cell row cell cos space x end cell equals cell cos space 109 comma 47 degree end cell row x equals cell 109 comma 47 degree plus k.360 degree end cell row blank blank blank row k equals 0 row blank rightwards double arrow cell x equals 109 comma 47 degree plus 0.360 degree end cell row blank equals cell 109 comma 47 degree end cell row blank blank blank row x equals cell negative 109 comma 47 degree plus k.360 degree end cell row blank blank blank row k equals 1 row blank rightwards double arrow cell x equals negative 109 comma 47 degree plus 1.360 degree end cell row blank equals cell 250 comma 53 degree end cell end table 

  •   sin space x equals 1 half 

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space x end cell equals cell 1 half end cell row cell sin space x end cell equals cell sin space 30 degree end cell row x equals cell 30 degree plus k.360 degree end cell row blank blank blank row k equals 0 row blank rightwards double arrow cell x equals 30 degree plus 0.360 degree end cell row x equals cell 30 degree end cell row blank blank blank row x equals cell left parenthesis 180 degree minus 30 degree right parenthesis plus k.360 degree end cell row blank equals cell 150 degree plus k.360 degree end cell row blank blank blank row k equals 0 row blank rightwards double arrow cell x equals 150 degree plus 0.360 degree end cell row blank equals cell 150 degree end cell end table  

Jadi, himpunan penyelesaian dari persamaan trigonometri tersebut adalah open curly brackets 30 degree space semicolon space 109 comma 47 degree space semicolon space 150 degree space semicolon space 250 comma 53 degree close curly brackets.

96

0.0 (0 rating)

Pertanyaan serupa

Buktikan bahwa cos x1+sin x​+1+sin xcos x​=cos x2​ dan cari semua besar sudut antara −180∘ dan 180∘ yang merupakan solusi dari persamaan (1+sinx)2+cos2x=4cos x (1+sin x).

45

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