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Himpunan penyelesaian dari persamaan sin space x minus sin space 2 x equals 0 untuk 0 degree less than x less than 360 degree adalah...

  1. open curly brackets 60 degree comma space 180 degree comma space 300 degree close curly brackets

  2. open curly brackets 60 degree comma space 150 degree comma space 300 degree close curly brackets

  3. open curly brackets 60 degree comma space 180 degree comma space 330 degree close curly brackets

  4. open curly brackets 30 degree comma space 180 degree comma space 330 degree close curly brackets

  5. open curly brackets 30 degree comma space 150 degree comma space 300 degree close curly brackets

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

Dengan menggunakan rumus trigonometri, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space x minus sin space 2 x end cell equals 0 row cell sin space x minus 2 sin space x times cos space x end cell equals 0 row cell sin space x times left parenthesis 1 minus 2 space cos space x right parenthesis end cell equals 0 row cell sin space x end cell equals 0 row cell sin space x end cell equals cell sin space 0 degree end cell row x equals cell space 0 degree plus n times 360 degree end cell row n equals cell 0 comma space 1 end cell row x equals cell space 0 degree plus 0 times 360 degree end cell row blank equals cell 0 degree end cell row x equals cell space 0 degree plus 1 times 360 degree end cell row blank equals cell 360 degree end cell row blank blank atau row x equals cell space 180 degree plus n times 360 degree end cell row n equals cell 0 comma space 1 end cell row x equals cell space 180 degree plus 0 times 360 degree end cell row blank equals cell 180 degree end cell row x equals cell space 180 degree plus 1 times 360 degree end cell row blank equals cell 540 degree space left parenthesis tidak space memenuhi right parenthesis end cell end table

 atau

table attributes columnalign right center left columnspacing 0px end attributes row cell 1 minus 2 space cos space x end cell equals 0 row cell negative 2 cos space x end cell equals cell negative 1 end cell row cell cos space x end cell equals cell 1 half end cell row cell cos space x end cell equals cell cos space 60 degree end cell row x equals cell 60 degree plus n times 360 degree end cell row n equals cell 0 comma space 1 end cell row x equals cell 60 degree plus 0 times 360 degree end cell row blank equals cell 60 degree end cell row x equals cell 60 degree plus 1 times 360 degree end cell row blank equals cell 420 degree space left parenthesis tidak space memenuhi right parenthesis end cell row blank blank atau row x equals cell negative 60 degree plus n times 360 degree end cell row n equals cell 0 comma 1 end cell row x equals cell negative 60 degree plus 0 times 360 degree end cell row blank equals cell negative 60 degree space left parenthesis tidak space memenuhi right parenthesis end cell row x equals cell negative 60 degree plus 1 times 360 degree end cell row blank equals cell 300 degree end cell end table

Dengan demikian,

 HP equals open curly brackets 60 degree comma space 180 degree comma space 300 degree close curly brackets


Oleh karena itu, jawaban yang benar adalah A.

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