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Selesaikan masing-masing persamaan trigonometri berikut untuk interval tertutup [0∘, 360∘]. c. 3 sin x.tan x+8=0

Pertanyaan

Selesaikan masing-masing persamaan trigonometri berikut untuk interval tertutup open square brackets 0 degree comma space 360 degree close square brackets.

c. 3 space sin space x. tan space x plus 8 equals 0    

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

himpunan penyelesaian dari persamaan trigonometri tersebut adalah open curly brackets 109 comma 47 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 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:

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 space sin space x. tan space x plus 8 end cell equals 0 row cell 3 space sin space x. fraction numerator sin space x over denominator cos space x end fraction plus 8 end cell equals 0 row cell fraction numerator 3 space sin squared x over denominator cos space x end fraction plus 8 end cell equals 0 row cell fraction numerator 3 space sin squared x plus 8 space cos space x over denominator cos space x end fraction end cell equals 0 row cell 3 space sin squared x plus 8 space cos space x end cell equals 0 row cell 3 left parenthesis 1 minus cos squared x right parenthesis plus 8 space cos space x end cell equals 0 row cell 3 minus 3 space cos squared space x plus 8 space cos space x end cell equals 0 row cell negative 3 space cos squared x plus 8 space cos space x plus 3 end cell equals 0 row cell 3 space cos squared x minus 8 space cos space x minus 3 end cell equals 0 row cell left parenthesis 3 space cos space x plus 1 right parenthesis left parenthesis cos space x minus 3 right parenthesis end cell equals 0 end table 

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cos 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 x 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 minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 1 third end cell 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 atau 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 cos 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 x 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 3 end table  

cos space x equals 3 tidak memenuhi karena negative 1 less or equal than cos space x less or equal than 1. Sehingga:

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 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  

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

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Selesaikan persamaan trigonometri di bawah ini, untuk 0∘≤x≤360∘. d. 7 secan x=9 cos x−3 tan x

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