Tentukan himpunan penyelesaian dari persamaan berikut untuk 0∘<x<360∘ sin(x+120∘)−sin(x−120∘)=213

Pertanyaan

Tentukan himpunan penyelesaian dari persamaan berikut untuk $0^\circ<x<360^\circ$

$\sin(x+120^\circ)-\sin(x-120^\circ)=\frac12\sqrt3$

Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Pembahasan

Dengan menggunakan rumus trigonometri, diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell sin left parenthesis x plus 120 right parenthesis degree minus sin left parenthesis x minus 120 right parenthesis degree end cell equals cell 1 half square root of 3 end cell row cell 2 cos space x degree times sin space 120 degree end cell equals cell 1 half square root of 3 end cell row cell 2 cos space x degree times sin space left parenthesis 180 degree minus 60 degree right parenthesis end cell equals cell 1 half square root of 3 end cell row cell 2 cos space x degree times open parentheses sin space 60 degree close parentheses end cell equals cell 1 half square root of 3 end cell row cell 2 cos space x degree times open parentheses 1 half square root of 3 close parentheses end cell equals cell 1 half square root of 3 end cell row cell 2 cos space x degree end cell equals cell fraction numerator 1 half square root of 3 over denominator 1 half square root of 3 end fraction end cell row cell cos space x degree end cell equals 1 row cell cos space x degree end cell equals cell 1 half end cell row cell cos space x degree end cell equals cell cos space 60 degree end cell end table$

maka:

Dengan demikian,

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

120

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