Roboguru

Pertanyaan

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

d. 7 space secan space x equals 9 space cos space x minus 3 space tan space x  

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

himpunan penyelesaian dari persamaan trigonometri tersebut adalah open curly brackets 19 comma 47 degree space semicolon space 160 comma 53 degree space semicolon space 221 comma 81 degree space semicolon space 318 comma 19 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 

Maka:

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell 7 space secan space x end cell equals cell 9 space cos space x minus 3 space tan space x end cell row cell fraction numerator 7 over denominator cos space x end fraction end cell equals cell 9 space cos space x minus 3 cross times fraction numerator sin space x over denominator cos space x end fraction space left parenthesis kedua space ruas cross times cos space x right parenthesis end cell row 7 equals cell 9 space cos squared x minus 3 space sin space x end cell row 0 equals cell 9 space cos squared x minus 3 space sin space x minus 7 end cell row 0 equals cell 9 left parenthesis 1 minus sin squared x right parenthesis minus 3 space sin space x minus 7 end cell row 0 equals cell 9 minus 9 space sin squared x minus 3 space sin space x minus 7 end cell row 0 equals cell negative 9 space sin squared x minus 3 space sin space x plus 2 end cell row 0 equals cell 9 space sin squared x plus 3 space sin space x minus 2 end cell row 0 equals cell left parenthesis 3 space sin space x plus 2 right parenthesis left parenthesis 3 space sin space x minus 1 right parenthesis end cell end table end style  

begin mathsize 12px style sin space x equals negative 2 over 3 space atau space sin space x equals 1 third end style   

  • sin space x equals negative 2 over 3  

  table attributes columnalign right center left columnspacing 0px end attributes row cell sin space x end cell equals cell negative 2 over 3 end cell row cell sin space x end cell equals cell sin space left parenthesis negative 41 comma 81 degree right parenthesis end cell row x equals cell negative 41 comma 81 degree plus k.360 degree end cell row blank blank blank row k equals 1 row blank rightwards double arrow cell x equals negative 41 comma 81 degree plus 1.360 degree end cell row blank equals cell 318 comma 19 degree end cell row blank blank blank row x equals cell left parenthesis 180 degree minus left parenthesis negative 41 comma 81 degree right parenthesis right parenthesis plus k.360 degree end cell row blank equals cell 221 comma 81 degree plus k.360 degree end cell row blank blank blank row k equals 0 row blank rightwards double arrow cell x equals 221 comma 81 degree plus k.360 degree end cell row blank equals cell 221 comma 81 degree plus 0.360 degree end cell row blank equals cell 221 comma 81 degree end cell end table  

  • sin space x equals 1 third  

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell sin space x equals 1 third sin space x equals sin space 19 comma 47 degree end cell row x equals cell 19 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 19 comma 47 degree plus 0.360 degree end cell row blank equals cell 19 comma 47 degree end cell row blank blank blank row x equals cell left parenthesis 180 degree minus 19 comma 47 degree right parenthesis plus k.360 degree end cell row blank equals cell 160 comma 53 degree plus k.360 degree end cell row blank blank blank row k equals 0 row x equals cell 160 comma 53 degree plus k.360 degree end cell row blank equals cell 160 comma 53 degree plus 0.360 degree end cell row blank equals cell 160 comma 53 degree end cell end table 

Jadi, himpunan penyelesaian dari persamaan trigonometri tersebut adalah open curly brackets 19 comma 47 degree space semicolon space 160 comma 53 degree space semicolon space 221 comma 81 degree space semicolon space 318 comma 19 degree close curly brackets.   

40

0.0 (0 rating)

Pertanyaan serupa

Himpunan nilai x yang memenuhi  dengan 23​π≤x≤2π adalah ....

6

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 Ruangguru

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