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Tentukan himpunan penyelesaian dari persamaan berikut untuk 0∘≤x≤360∘ sinx∘+sin5x∘=sin3x∘

Pertanyaan

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

sin space x degree plus sin space 5 x degree equals sin space 3 x degree

Pembahasan Video:

Pembahasan:

Dengan menggunakan rumus trigonometri, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space x degree plus sin space 5 x degree end cell equals cell sin space 3 x degree end cell row cell sin space x degree plus sin space 5 x degree minus sin space 3 x degree end cell equals 0 row cell 2 sin open parentheses fraction numerator x degree plus 5 x degree over denominator 2 end fraction close parentheses cos open parentheses fraction numerator x degree minus 5 x degree over denominator 2 end fraction close parentheses minus sin space 3 x degree end cell equals 0 row cell 2 sin space 3 x degree times cos left parenthesis negative 2 x degree right parenthesis minus sin space 3 x degree end cell equals 0 row cell sin space 3 x degree open parentheses 2 cos left parenthesis negative 2 x degree right parenthesis minus 1 close parentheses end cell equals 0 row cell sin space 3 x degree end cell equals cell 0 space atau end cell row cell 2 cos left parenthesis negative 2 x degree right parenthesis minus 1 end cell equals 0 row cell cos left parenthesis negative 2 x degree right parenthesis end cell equals cell 1 half end cell end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space 3 x degree end cell equals 0 row cell sin space 3 x degree end cell equals cell sin space 0 degree end cell row cell 3 x degree end cell equals cell 0 degree plus n times 360 degree end cell row cell x degree end cell equals cell 0 degree plus n times 120 degree end cell row n equals cell 0 comma space 1 comma space 2 comma space 3 end cell row cell x degree end cell equals cell 0 degree plus 0 times 120 degree end cell row blank equals cell 0 degree end cell row cell x degree end cell equals cell 0 degree plus 1 times 120 degree end cell row blank equals cell 360 degree end cell row cell x degree end cell equals cell 0 degree plus 2 times 120 degree end cell row blank equals cell 240 degree end cell row cell x degree end cell equals cell 0 degree plus 3 times 120 degree end cell row blank equals cell 360 degree end cell row blank blank atau row cell 3 straight x degree end cell equals cell 180 degree plus straight n times 360 degree end cell row cell straight x degree end cell equals cell 60 degree plus straight n times 120 degree end cell row straight n equals cell 0 comma space 1 comma space 2 end cell row cell straight x degree end cell equals cell 60 degree plus 0 times 120 degree end cell row blank equals cell 60 degree end cell row cell straight x degree end cell equals cell 60 degree plus 1 times 120 degree end cell row blank equals cell 180 degree end cell row cell straight x degree end cell equals cell 60 degree plus 2 times 120 degree end cell row blank equals cell 300 degree end cell end table

atau

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space left parenthesis negative 2 x degree right parenthesis end cell equals cell cos space 2 x degree end cell row cell cos space 2 x degree end cell equals cell 1 half end cell row cell cos space 2 x degree end cell equals cell cos space 60 degree end cell row cell 2 x degree end cell equals cell 60 degree plus n times 360 degree end cell row cell x degree end cell equals cell 30 degree plus n times 180 degree end cell row n equals cell 0 comma space 1 end cell row cell x degree end cell equals cell 30 degree plus 0 times 180 degree end cell row blank equals cell 30 degree end cell row cell x degree end cell equals cell 30 degree plus 1 times 180 degree end cell row blank equals cell 210 degree end cell row blank blank atau row cell x degree end cell equals cell negative 30 degree plus n times 180 degree end cell row n equals cell 0 comma space 1 comma space 2 end cell row cell x degree end cell equals cell negative 30 degree plus 0 times 180 degree end cell row blank equals cell negative 30 degree end cell row cell x degree end cell equals cell negative 30 degree plus 1 times 180 degree end cell row blank equals cell 150 degree end cell row cell x degree end cell equals cell negative 30 degree plus 2 times 180 degree end cell row blank equals cell 330 degree end cell end table

Dengan demikian, 

HP equals open curly brackets 0 degree comma space 30 degree comma space 60 degree comma space 120 degree comma space 150 degree comma space 180 degree comma space 210 degree comma space 240 degree comma space 300 degree comma space 330 degree comma space 360 degree close curly brackets

Jawaban terverifikasi

Dijawab oleh:

N. Puspita

Terakhir diupdate 07 Oktober 2021

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