Tentukan himpunan penyelesaian dari persamaan berikut untuk 0∘<x<360∘ sin(x+120∘)−sin(x−120∘)=21​3​

Pertanyaan

Tentukan himpunan penyelesaian dari persamaan berikut untuk 0 degree less than x less than 360 degree

sin left parenthesis x plus 120 degree right parenthesis minus sin left parenthesis x minus 120 degree right parenthesis equals 1 half square root of 3

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:

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

Dengan demikian, 

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

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Selesaikanlah persamaan berikut untuk 0∘<x<360∘ sin (x+120)∘−sin (x−60)∘=0

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