Pertanyaan

Selesaikanlah persamaan berikut untuk 0 ∘ ≤ x ≤ 36 0 ∘ sin x ∘ + 5 cos x ∘ = 2

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

$sin x^{\circ} + 5 cos x^{\circ} = 2$

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Klaim

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

Dengan mengggunakan rumus trigonometri, misalkan, Sehingga, Kemudian, Dengan demikian, .

Dengan mengggunakan rumus trigonometri, misalkan,

table attributes columnalign right center left columnspacing 0px end attributes row cell sin space x plus 5 cos 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,

$table attributes columnalign right center left columnspacing 0px end attributes row cell k cos space alpha degree end cell equals 5 row cell k sin space alpha degree end cell equals cell negative 1 end cell row k equals cell square root of open parentheses 5 close parentheses squared plus open parentheses negative 1 close parentheses squared end root end cell row blank equals cell square root of 25 plus 1 end root end cell row blank equals cell square root of 26 end cell row cell tan space alpha degree end cell equals cell fraction numerator negative 1 over denominator 5 end fraction space left parenthesis kuadran space IV right parenthesis end cell row cell alpha degree end cell equals cell 348 comma 69 degree end cell end table$

Kemudian,

$table attributes columnalign right center left columnspacing 0px end attributes row cell k cos space left parenthesis x plus alpha right parenthesis degree end cell equals cell square root of 26 cos space left parenthesis x plus 348 comma 69 right parenthesis degree equals square root of 2 end cell row blank left right double arrow cell cos space left parenthesis x plus 348 comma 69 right parenthesis degree equals fraction numerator square root of 2 over denominator square root of 26 end fraction end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell cos space left parenthesis x plus 348 comma 69 right parenthesis degree end cell equals cell fraction numerator 1 over denominator square root of 13 end fraction end cell row cell cos space left parenthesis x plus 348 comma 69 right parenthesis degree end cell equals cell cos space 73 comma 90 degree end cell row cell space x plus 348 comma 69 degree end cell equals cell plus-or-minus 73 comma 90 degree plus n times 360 degree end cell row x equals cell negative 274 comma 79 degree plus n times 360 degree end cell row cell untuk space n end cell equals cell 0 comma space 1 end cell row x equals cell negative 274 comma 79 degree plus 0 times 360 degree end cell row blank equals cell negative 274 comma 79 degree end cell row x equals cell negative 274 comma 79 degree plus 1 times 360 degree end cell row blank equals cell 85 comma 21 degree end cell row cell atau space x end cell equals cell negative 422 comma 59 degree plus n times 360 degree end cell row n equals cell 0 comma space 1 comma space 2 end cell row x equals cell negative 422 comma 59 degree plus 0 times 360 degree end cell row blank equals cell negative 422 comma 59 degree end cell row x equals cell negative 422 comma 59 degree plus 1 times 360 degree end cell row blank equals cell negative 62 comma 59 degree end cell row x equals cell negative 422 comma 59 degree plus 2 times 360 degree end cell row blank equals cell 297 comma 41 degree end cell end table$

Dengan demikian,

table attributes columnalign right center left columnspacing 0px end attributes row HP equals cell open curly brackets 85 comma 21 degree comma space 297 comma 41 degree close curly brackets end cell end table .