Selesaikanlah persamaan berikut untuk 0∘<x<360∘ cos 3x∘+cos (x+60)∘=0

Pertanyaan

Selesaikanlah persamaan berikut untuk 0 degree less than x less than 360 degree

cos space 3 x degree plus cos space open parentheses x plus 60 close parentheses degree equals 0

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 cos space 3 x degree plus cos space open parentheses x plus 60 close parentheses degree end cell equals 0 row cell 2 cos open parentheses fraction numerator 3 x plus x plus 60 over denominator 2 end fraction close parentheses times cos space open parentheses fraction numerator 3 x minus x minus 60 over denominator 2 end fraction close parentheses end cell equals 0 row cell 2 cos open parentheses 2 x plus 30 close parentheses times cos open parentheses x minus 30 close parentheses end cell equals 0 row cell cos open parentheses 2 x plus 30 close parentheses times cos open parentheses x minus 30 close parentheses end cell equals 0 end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space left parenthesis 2 x plus 30 right parenthesis degree end cell equals 0 row cell cos space left parenthesis 2 x plus 30 right parenthesis degree end cell equals cell cos space 0 degree end cell row cell 2 x plus 30 degree end cell equals cell plus-or-minus 90 degree plus n times 360 degree end cell row cell 2 x end cell equals cell 60 degree plus n times 360 degree end cell row x equals cell 30 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 30 degree plus 0 times 180 degree end cell row blank equals cell 30 degree end cell row x equals cell 30 degree plus 1 times 180 degree end cell row blank equals cell 210 degree end cell row cell atau space x end cell equals cell negative 60 degree plus n times 180 degree end cell row cell untuk space n end cell equals cell 0 comma space 1 comma space 2 end cell row cell space x end cell equals cell negative 60 degree plus 0 times 180 degree end cell row blank equals cell negative 60 degree end cell row x equals cell negative 60 degree plus 1 times 180 degree end cell row blank equals cell 120 degree end cell row x equals cell negative 60 degree plus 2 times 180 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 x minus 30 right parenthesis degree end cell equals 0 row cell cos space left parenthesis x minus 30 right parenthesis degree end cell equals cell cos space 90 degree end cell row cell x minus 30 degree end cell equals cell plus-or-minus 90 degree plus n times 360 degree end cell row x equals cell 120 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 120 degree plus 0 times 360 degree end cell row blank equals cell 120 degree end cell row x equals cell 120 degree plus 1 times 360 degree end cell row blank equals cell 480 degree end cell row cell atau space x end cell equals cell negative 60 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 negative 60 degree plus 0 times 360 degree end cell row blank equals cell negative 60 degree end cell row x equals cell negative 60 degree plus 1 times 360 degree end cell row blank equals cell 300 degree end cell end table

Dengan demikian,

HP equals open curly brackets 30 degree comma space 120 degree comma space 210 degree comma space 300 degree close curly brackets

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