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Pertanyaan

Selesaikan persamaan berikut untuk 0 degree less or equal than x less or equal than 360 degree

sin space 2 x degree minus 2 sin space x degree equals 0

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

 HP equals open curly brackets 0 degree comma space 180 degree comma space 360 degree close curly brackets.

Pembahasan

Ingat!

sin space 2 x degree equals 2 space sin space x degree times cos space x degree

dan

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space a end cell equals cell sin space p degree space left right arrow open curly brackets table attributes columnalign left end attributes row cell a equals p degree plus k open parentheses 360 degree close parentheses end cell row cell a equals open parentheses 180 minus p close parentheses degree plus k open parentheses 360 degree close parentheses end cell end table close end cell row cell cos space a end cell equals cell cos space p space left right arrow a equals plus-or-minus p degree plus k open parentheses 360 degree close parentheses end cell end table 

Dengan menggunakan rumus trigonometri di atas, maka diperoleh perhitungan sebagai berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 2 x degree minus 2 sin space x degree end cell equals 0 row cell 2 sin space x degree times cos space x degree minus 2 sin x degree end cell equals 0 row cell 2 sin space x degree open parentheses cos space x degree minus 1 close parentheses end cell equals 0 end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 sin space x degree end cell equals cell 0 space space space atau space space space space cos space x degree minus 1 equals 0 end cell row cell space space sin space x degree end cell equals cell 0 space space space space space space space space space space space space space space space space space space space space cos space x degree equals 1 space end cell end table 

Untuk sin space x degree equals 0, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space x degree end cell equals 0 row cell sin space x degree end cell equals cell sin space 0 degree space left right arrow open curly brackets table row cell x equals 0 plus k open parentheses 360 close parentheses end cell row cell x equals 180 plus k open parentheses 360 close parentheses end cell end table close end cell end table 

Subtitusi nilai k, sehingga: 

table attributes columnalign right center left columnspacing 0px end attributes row cell text Untuk  end text x end cell equals cell 0 plus k open parentheses 360 close parentheses end cell row k equals cell 0 left right arrow x equals 0 end cell row k equals cell 1 left right arrow x equals 360 end cell row cell text Untuk  end text x end cell equals cell 180 plus k open parentheses 360 close parentheses end cell row k equals cell 0 left right arrow x equals 180 end cell end table      

Untuk cos space x degree equals 1, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space x degree end cell equals 1 row cell cos space x degree end cell equals cell cos space 0 degree end cell row blank left right arrow cell x equals plus-or-minus 0 plus k open parentheses 360 close parentheses end cell row x equals cell k open parentheses 360 close parentheses end cell end table   

Subtitusi nilai k, sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row x equals cell k open parentheses 360 close parentheses end cell row cell text untuk end text space k end cell equals cell 0 space left right arrow x equals 0 end cell row k equals cell 1 space left right arrow x equals 360 end cell end table  

Dengan demikian, HP equals open curly brackets 0 degree comma space 180 degree comma space 360 degree close curly brackets.

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