Tentukan himpunan penyelesaian dari persamaan berikut untuk 0∘<x<360∘ sin 4x+sin 2x=0

Pertanyaan

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

sin space 4 x plus sin space 2 x equals 0

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

Pembahasan

Dengan menggunakan rumus trigonometri, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 4 x plus sin space 2 x end cell equals 0 row cell 2 space sin 2 x times cos space 2 x plus sin space 2 x end cell equals 0 row cell sin space 2 x times left parenthesis 2 cos space 2 x plus 1 right parenthesis end cell equals 0 end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 2 x end cell equals 0 row cell sin space 2 x end cell equals cell sin space 0 degree end cell row cell 2 x end cell equals cell 0 degree plus n times 360 degree end cell row cell x subscript 1 end cell equals cell 0 degree plus n times 180 degree end cell row cell x subscript 2 end cell equals cell 90 degree plus n times 180 degree end cell row n equals cell 0 comma space 1 end cell row cell x subscript 1 end cell equals cell 0 degree plus 0 times 180 degree end cell row blank equals cell 0 degree end cell row cell x subscript 1 end cell equals cell 0 degree plus 1 times 180 degree end cell row blank equals cell 180 degree end cell row cell x subscript 2 end cell equals cell 90 degree plus 0 times 180 degree end cell row blank equals cell 90 degree end cell row cell x subscript 2 end cell equals cell 90 degree plus 1 times 180 degree end cell row blank equals cell 270 degree end cell end table

atau

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 space cos space 2 x plus 1 end cell equals 0 row cell 2 cos space 2 x end cell equals cell negative 1 end cell row cell cos space 2 x end cell equals cell negative 1 half end cell row cell cos space 2 x end cell equals cell cos space 120 degree end cell row cell 2 x end cell equals cell 120 degree plus n times 360 degree end cell row cell x subscript 1 end cell equals cell 60 degree plus n times 180 degree end cell row cell x subscript 2 end cell equals cell negative 60 degree plus n times 180 degree end cell row n equals cell 0 comma space 1 comma space 2 end cell row cell x subscript 1 end cell equals cell 60 degree plus 0 times 180 degree end cell row blank equals cell 60 degree end cell row cell x subscript 1 end cell equals cell 60 degree plus 1 times 180 degree end cell row blank equals cell 240 degree end cell row cell x subscript 2 end cell equals cell negative 60 degree plus 0 times 180 degree end cell row blank equals cell negative 60 degree end cell row cell x subscript 2 end cell equals cell negative 60 degree plus 1 times 180 degree end cell row blank equals cell 120 degree end cell row cell x subscript 2 end cell equals cell negative 60 degree plus 2 times 180 degree end cell row blank equals cell 300 degree end cell end table

Dengan demikian, 

HP equals open curly brackets 60 degree comma space 90 degree comma space 120 degree comma space 180 degree comma space 240 degree comma space 270 degree comma space 300 degree close curly brackets

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Selesaikan persamaan berikut untuk 0∘≤x≤360∘ sin 2x∘−2sin x∘=0

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Jawaban terverifikasi

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