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Himpunan penyelesaian dari persamaan cos (61​π−x)=cos (31​π−x) untuk 0≤x≤2π adalah...

Pertanyaan

Himpunan penyelesaian dari persamaan cos space open parentheses 1 over 6 straight pi minus straight x close parentheses equals cos space open parentheses 1 third straight pi minus straight x close parentheses untuk 0 less or equal than x less or equal than 2 straight pi adalah...

  1. open curly brackets 3 over 4 straight pi comma space 5 over 4 straight pi close curly brackets

  2. open curly brackets 1 half straight pi comma space 3 over 4 straight pi close curly brackets

  3. open curly brackets 1 half straight pi comma space 5 over 4 straight pi close curly brackets

  4. open curly brackets 1 fourth straight pi comma space 3 over 4 straight pi close curly brackets

  5. open curly brackets 1 fourth straight pi comma space 5 over 4 straight pi close curly brackets

Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Jawaban

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Pembahasan

Dengan menggunakan konsep trigonometri, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space open parentheses 1 over 6 straight pi minus straight x close parentheses end cell equals cell cos space open parentheses 1 third straight pi minus straight x close parentheses end cell row cell cos space open parentheses 1 over 6 straight pi minus straight x close parentheses minus cos space open parentheses 1 third straight pi minus straight x close parentheses end cell equals 0 row cell negative 2 sin open parentheses fraction numerator 1 over 6 straight pi minus straight x plus 1 third straight pi minus straight x over denominator 2 end fraction close parentheses sin open parentheses fraction numerator 1 over 6 straight pi minus straight x minus 1 third straight pi plus straight x over denominator 2 end fraction close parentheses end cell equals 0 row cell negative 2 sin open parentheses fraction numerator 30 minus x plus 60 minus x over denominator 2 end fraction close parentheses sin open parentheses fraction numerator 30 minus x minus 60 plus x over denominator 2 end fraction close parentheses end cell equals 0 row cell negative 2 sin open parentheses 45 minus x close parentheses sin open parentheses negative 15 close parentheses end cell equals 0 row cell sin open parentheses 45 minus x 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 45 minus x right parenthesis end cell equals 0 row cell sin space left parenthesis 45 minus x right parenthesis end cell equals cell sin space 0 degree end cell row cell 45 minus x end cell equals cell 0 degree plus n times 360 degree end cell row cell negative x end cell equals cell negative 45 degree plus n times 360 degree end cell row x equals cell 45 degree minus n times 360 degree end cell row cell untuk space n end cell equals 0 row x equals cell 45 degree minus 0 times 360 degree end cell row blank equals cell 45 degree end cell row cell atau space 45 minus x end cell equals cell 180 degree plus n times 360 degree end cell row cell negative x end cell equals cell 135 degree plus n times 360 degree end cell row x equals cell negative 135 degree minus n times 360 degree space left parenthesis tidak space memenuhi right parenthesis end cell end table

Dengan demikian,

table attributes columnalign right center left columnspacing 0px end attributes row HP equals cell open curly brackets 45 degree close curly brackets end cell row blank equals cell open curly brackets 1 fourth straight pi close curly brackets end cell end table


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