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Selesaikanlah persamaan berikut untuk 0 ∘ < x < 36 0 ∘ sin ( 3 x − 45 ) ∘ + sin ( x − 15 ) ∘ = 0

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Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Pembahasan

Dengan menggunakan rumus trigonometri, diperoleh: Sehingga, atau Dengan demikian,

Dengan menggunakan rumus trigonometri, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space open parentheses 3 x minus 45 close parentheses degree plus sin space open parentheses x minus 15 close parentheses degree end cell equals 0 row cell 2 sin open parentheses fraction numerator 3 x minus 45 plus x minus 15 over denominator 2 end fraction close parentheses times sin open parentheses fraction numerator 3 x minus 45 minus x plus 15 over denominator 2 end fraction close parentheses end cell equals 0 row cell 2 sin open parentheses 2 x minus 30 close parentheses times sin open parentheses x minus 15 close parentheses end cell equals 0 row cell sin open parentheses 2 x minus 30 close parentheses times sin open parentheses x minus 15 close parentheses end cell equals 0 end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space left parenthesis 2 x minus 30 right parenthesis end cell equals 0 row cell sin space left parenthesis 2 x minus 30 right parenthesis end cell equals cell sin space 0 degree end cell row cell 2 x minus 30 end cell equals cell 0 degree plus n times 360 degree end cell row cell 2 x end cell equals cell 30 degree plus n times 360 degree end cell row x equals cell 15 degree plus n times 180 degree end cell row cell untuk space n end cell equals cell 0 comma space 1 end cell row x equals cell 15 degree plus 0 times 180 degree end cell row blank equals cell 15 degree end cell row x equals cell 15 degree plus 1 times 180 degree end cell row blank equals cell 195 degree end cell row cell atau space 2 x minus 30 end cell equals cell open parentheses 180 minus 0 close parentheses degree plus n times 360 degree end cell row blank equals cell 180 degree plus n times 360 degree end cell row cell 2 x end cell equals cell 210 degree plus n times 360 degree end cell row x equals cell 105 degree plus n times 180 degree end cell row cell untuk space n end cell equals cell 0 comma space 1 end cell row x equals cell 105 degree plus 0 times 180 degree end cell row blank equals cell 105 degree end cell row x equals cell 105 degree plus 1 times 180 degree end cell row blank equals cell 285 degree end cell end table

atau

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space left parenthesis x minus 15 right parenthesis end cell equals 0 row cell sin space left parenthesis x minus 15 right parenthesis end cell equals cell sin space 0 degree end cell row cell x minus 15 end cell equals cell 0 degree plus n times 360 degree end cell row x equals cell 15 degree plus n times 360 degree end cell row cell untuk space n end cell equals cell 0 comma space 1 end cell row x equals cell 15 degree plus 0 times 360 degree end cell row blank equals cell 15 degree end cell row x equals cell 15 degree plus 1 times 360 degree end cell row blank equals cell 375 degree end cell row cell atau space x minus 15 end cell equals cell open parentheses 180 minus 0 close parentheses degree plus n times 360 degree end cell row blank equals cell 195 degree plus n times 360 degree end cell row cell untuk space n end cell equals cell 0 comma space 1 end cell row x equals cell 195 degree plus 0 times 360 degree end cell row blank equals cell 195 degree end cell row x equals cell 195 degree plus 1 times 360 degree end cell row blank equals cell 555 degree end cell end table

Dengan demikian,

HP equals open curly brackets 15 degree comma space 105 degree comma space 195 degree comma space 285 degree close curly brackets

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