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Himpunan penyelesaian dari persamaan cos x + 3 ​ tan 3 0 ∘ = 2 sin 2 1 ​ x ⋅ cos 2 1 ​ x untuk 0 ∘ ≤ x ≤ 36 0 ∘ adalah...

Himpunan penyelesaian dari persamaan  untuk  adalah...

  1. open curly brackets 30 degree comma space 60 degree comma space 180 degree close curly brackets

  2. open curly brackets 45 degree comma space 90 degree comma space 180 degree close curly brackets

  3. open curly brackets 90 degree comma space 135 degree comma space 180 degree close curly brackets

  4. open curly brackets 90 degree comma space 180 degree close curly brackets

  5. open curly brackets 90 degree comma space 270 degree close curly brackets

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Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

jawaban yang benar adalah D.

Pembahasan

Dengan mengggunakan rumus trigonometri, diperoleh: Misalkan, Sehingga, Kemudian, Jadi, . Oleh karena itu, jawaban yang benar adalah D.

Dengan mengggunakan rumus trigonometri, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space x plus square root of 3 tan space 30 degree end cell equals cell 2 sin 1 half x times cos 1 half x end cell row cell cos space x plus square root of 3 times fraction numerator 1 over denominator square root of 3 end fraction end cell equals cell 2 sin 1 half x times cos 1 half x end cell row cell cos space x plus 1 end cell equals cell 2 sin 1 half x times cos 1 half x end cell row cell cos space x plus 1 end cell equals cell sin 2 times 1 half x end cell row cell cos space x plus 1 end cell equals cell sin x end cell row cell cos space x minus sin space x end cell equals cell negative 1 end cell end table

Misalkan,

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space x minus sin space x end cell equals cell k cos left parenthesis x plus alpha right parenthesis degree end cell row blank equals cell k cos space x degree times cos space alpha degree minus k sin space x degree times sin space alpha degree end cell end table

Sehingga,

table attributes columnalign right center left columnspacing 0px end attributes row cell k cos space alpha degree end cell equals 1 row cell k sin space alpha degree end cell equals 1 row k equals cell square root of open parentheses 1 close parentheses squared plus open parentheses 1 close parentheses squared end root end cell row blank equals cell square root of 2 end cell row cell tan space alpha degree end cell equals cell 1 over 1 left parenthesis kuadran space straight I right parenthesis end cell row cell alpha degree end cell equals cell 45 degree end cell end table

Kemudian,

table attributes columnalign right center left columnspacing 0px end attributes row cell k cos space left parenthesis x plus alpha right parenthesis degree end cell equals cell square root of 2 cos space left parenthesis x plus 45 right parenthesis degree equals negative 1 end cell row blank left right double arrow cell cos space left parenthesis x plus 45 right parenthesis degree equals fraction numerator negative 1 over denominator square root of 2 end fraction end cell row cell cos space left parenthesis x plus 45 right parenthesis degree end cell equals cell fraction numerator negative 1 over denominator square root of 2 end fraction end cell row cell cos space left parenthesis x plus 45 right parenthesis degree end cell equals cell cos space 135 degree end cell row cell space x plus 45 degree end cell equals cell plus-or-minus 135 degree plus n times 360 degree end cell row x equals cell 90 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 90 degree plus 0 times 360 degree end cell row blank equals cell 90 degree end cell row x equals cell 90 degree plus 1 times 360 degree end cell row blank equals cell 450 degree end cell row cell atau space x end cell equals cell negative 180 degree plus n times 360 degree end cell row n equals cell 0 comma space 1 end cell row x equals cell negative 180 degree plus 0 times 360 degree end cell row blank equals cell negative 180 degree end cell row x equals cell negative 180 degree plus 1 times 360 degree end cell row blank equals cell 180 degree end cell end table

Jadi, HP equals open curly brackets 90 degree comma space 180 degree close curly brackets.

Oleh karena itu, jawaban yang benar adalah D.

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Selesaikanlah persamaan berikut untuk 0 ∘ < x < 36 0 ∘ 3 sin 2 x + 4 sin x ⋅ cos x − cos 2 x = 2

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