Pertanyaan

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

Selesaikanlah persamaan berikut untuk $0^{\circ} < x < 36 0^{\circ}$

$3 sin^{2} x + 4 sin x \cdot cos x - cos^{2} x = 2$

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Klaim

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

Dengan menggunakan rumus trigonommetri, diperoleh: Kemudian misalkan, Sehingga, Kemudian, Dengan demikian, .

Dengan menggunakan rumus trigonommetri, diperoleh:

Kemudian misalkan,

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 2 cos space 2 x plus 2 sin space 2 x end cell equals cell k cos left parenthesis 2 x plus alpha right parenthesis degree end cell row blank equals cell k cos space 2 x degree times cos space alpha degree minus k sin space 2 x degree times sin space alpha degree end cell end table

Sehingga,

$table attributes columnalign right center left columnspacing 0px end attributes row cell k cos space alpha degree end cell equals cell negative 2 end cell row cell k sin space alpha degree end cell equals cell negative 2 end cell row k equals cell square root of open parentheses negative 2 close parentheses squared plus open parentheses negative 2 close parentheses squared end root end cell row blank equals cell square root of 4 plus 4 end root end cell row blank equals cell 2 square root of 2 end cell row cell tan space alpha degree end cell equals cell fraction numerator negative 2 over denominator negative 2 end fraction space left parenthesis kuadran space III right parenthesis end cell row cell alpha degree end cell equals cell 225 degree end cell end table$

Kemudian,

$table attributes columnalign right center left columnspacing 0px end attributes row cell k cos space left parenthesis 2 x plus alpha right parenthesis degree end cell equals cell 2 square root of 2 cos space left parenthesis 2 x plus 225 right parenthesis degree equals 1 end cell row blank left right double arrow cell cos space left parenthesis 2 x plus 225 right parenthesis degree equals fraction numerator 1 over denominator 2 square root of 2 end fraction end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos space left parenthesis 2 x plus 225 right parenthesis degree end cell equals cell fraction numerator 1 over denominator 2 square root of 2 end fraction end cell row cell cos space left parenthesis 2 x plus 225 right parenthesis degree end cell equals cell cos space 69 comma 3 degree end cell row cell space 2 x plus 225 degree end cell equals cell plus-or-minus 69 comma 3 degree plus n times 360 degree end cell row cell 2 x end cell equals cell negative 155 comma 7 degree plus n times 360 degree end cell row x equals cell negative 77 comma 85 degree plus n times 180 degree end cell row cell untuk space n end cell equals cell 0 comma space 1 comma space 2 end cell row x equals cell negative 77 comma 85 degree plus 0 times 180 degree end cell row blank equals cell negative 77 comma 85 degree end cell row x equals cell negative 77 comma 85 degree plus 1 times 180 degree end cell row blank equals cell 102 comma 15 degree end cell row x equals cell negative 77 comma 85 degree plus 2 times 180 degree end cell row blank equals cell 282 comma 15 degree end cell row cell atau space 2 x end cell equals cell negative 294 comma 3 degree plus n times 360 degree end cell row x equals cell negative 147 comma 15 degree plus n times 180 degree end cell row n equals cell 0 comma space 1 comma space 2 end cell row x equals cell negative 147 comma 15 degree plus 0 times 180 degree end cell row blank equals cell negative 147 comma 15 degree end cell row x equals cell negative 147 comma 15 degree plus 1 times 180 degree end cell row blank equals cell 32 comma 85 degree end cell row x equals cell negative 147 comma 15 degree plus 2 times 180 degree end cell row blank equals cell 212 comma 85 degree end cell end table$

Dengan demikian,

table attributes columnalign right center left columnspacing 0px end attributes row HP equals cell open curly brackets 32 comma 85 degree comma space 102 comma 15 degree comma space 212 comma 85 degree comma space 282 comma 15 degree close curly brackets end cell end table .

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