Pertanyaan

Himpunan penyelesaian dari persamaan cos 2 x + cos ( 2 x + 3 1 π ) = 0 untuk π ≤ x ≤ 2 π adalah...

Himpunan penyelesaian dari persamaan $cos 2 x + cos (2 x + \frac{1}{3} π) = 0$ untuk $π \leq x \leq 2 π$ adalah...

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Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Dengan menggunakan rumus trigonometri diperoleh: Sehingga, atau Dengan demikian, Oleh karena itu, jawaban yang benar adalah C.

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.