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

Pertanyaan

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

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

  2. open curly brackets 3 over 2 straight pi comma space 5 over 3 straight pi close curly brackets

  3. open curly brackets 7 over 6 straight pi comma space 5 over 3 straight pi close curly brackets

  4. open curly brackets 7 over 6 straight pi comma space 4 over 3 straight pi close curly brackets

  5. open curly brackets 7 over 6 straight pi comma space 3 over 2 straight pi close curly brackets

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Dengan menggunakan rumus trigonometri diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space 2 x plus cos space open parentheses 2 x plus 1 third straight pi close parentheses end cell equals 0 row cell 2 cos space open parentheses fraction numerator 2 x plus 2 x plus 1 third straight pi over denominator 2 end fraction close parentheses times cos space open parentheses fraction numerator 2 x minus 2 x minus 1 third straight pi over denominator 2 end fraction close parentheses end cell equals 0 row cell 2 cos space open parentheses fraction numerator 4 x plus 1 third straight pi over denominator 2 end fraction close parentheses times cos space open parentheses fraction numerator negative 1 third straight pi over denominator 2 end fraction close parentheses end cell equals 0 row cell 2 cos space open parentheses 2 x plus 1 over 6 straight pi close parentheses times cos space open parentheses negative 1 over 6 straight pi close parentheses end cell equals 0 row cell 2 cos space open parentheses 2 x plus 1 over 6 straight pi close parentheses times 1 half square root of 3 end cell equals 0 row cell square root of 3 cos space open parentheses 2 x plus 1 over 6 straight pi close parentheses end cell equals 0 row cell cos space open parentheses 2 x plus 1 over 6 straight pi close parentheses end cell equals 0 row cell cos space open parentheses 2 x plus 1 over 6 straight pi close parentheses end cell equals cell cos space 1 half straight pi end cell end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x plus straight pi over 6 end cell equals cell straight pi over 2 plus n times 2 straight pi end cell row cell 2 x end cell equals cell straight pi over 2 minus straight pi over 6 plus n times 2 straight pi end cell row cell 2 x end cell equals cell straight pi over 3 plus n times 2 straight pi end cell row x equals cell straight pi over 6 plus n times straight pi end cell row x equals cell straight pi over 6 plus 0 times straight pi end cell row blank equals cell straight pi over 6 end cell row straight x equals cell straight pi over 6 plus 1 times straight pi end cell row blank equals cell fraction numerator 7 straight pi over denominator 6 end fraction end cell end table

atau

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x plus straight pi over 6 end cell equals cell negative straight pi over 2 plus n times 2 straight pi end cell row cell 2 x end cell equals cell negative straight pi over 2 minus straight pi over 6 plus n times 2 straight pi end cell row cell 2 x end cell equals cell negative fraction numerator 2 straight pi over denominator 3 end fraction plus n times 2 straight pi end cell row x equals cell negative straight pi over 3 plus n times straight pi end cell row x equals cell negative straight pi over 3 plus 0 times straight pi end cell row blank equals cell negative straight pi over 3 end cell row straight x equals cell negative straight pi over 3 plus 1 times straight pi end cell row blank equals cell fraction numerator 2 straight pi over denominator 3 end fraction end cell row straight x equals cell negative straight pi over 3 plus 2 times straight pi end cell row blank equals cell fraction numerator 5 straight pi over denominator 3 end fraction end cell end table

Dengan demikian, 

HP equals open curly brackets fraction numerator 7 straight pi over denominator 6 end fraction comma space fraction numerator 5 straight pi over denominator 3 end fraction close curly brackets

Oleh karena itu, jawaban yang benar adalah C.

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