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Selesaikanlah persamaan berikut untuk 0 ∘ ≤ x ≤ 36 0 ∘ 3 cos x ∘ − 4 sin x ∘ = 1

Selesaikanlah persamaan berikut untuk 

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A. Acfreelance

Master Teacher

Jawaban terverifikasi

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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 3 cos space x minus 4 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 plus 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 3 row cell k sin space alpha degree end cell equals 4 row k equals cell square root of open parentheses 3 close parentheses squared plus open parentheses 4 close parentheses squared end root end cell row blank equals cell square root of 9 plus 16 end root end cell row blank equals cell square root of 25 end cell row blank equals 5 row cell tan space alpha degree end cell equals cell 4 over 3 space left parenthesis kuadran space straight I right parenthesis end cell row cell alpha degree end cell equals cell 53 comma 13 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 5 cos space left parenthesis x plus 53 comma 13 right parenthesis degree equals 1 end cell row blank left right double arrow cell cos space left parenthesis x plus 53 comma 13 right parenthesis degree equals 1 fifth end cell row cell cos space left parenthesis x plus 53 comma 13 right parenthesis degree end cell equals cell 1 fifth end cell row cell cos space left parenthesis x plus 53 comma 13 right parenthesis degree end cell equals cell cos space 78 comma 46 degree end cell row cell space x plus 53 comma 13 degree end cell equals cell plus-or-minus 78 comma 46 degree plus n times 360 degree end cell row x equals cell 25 comma 33 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 25 comma 33 degree plus 0 times 360 degree end cell row blank equals cell 25 comma 33 degree end cell row x equals cell 25 comma 33 degree plus 1 times 360 degree end cell row blank equals cell 385 comma 33 degree end cell row cell atau space x end cell equals cell negative 131 comma 59 degree plus n times 360 degree end cell row n equals cell 0 comma space 1 end cell row x equals cell negative 131 comma 59 degree plus 0 times 360 degree end cell row blank equals cell negative 131 comma 59 degree end cell row x equals cell negative 131 comma 59 degree plus 1 times 360 degree end cell row blank equals cell 228 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 25 comma 33 degree comma space 228 comma 41 degree close curly brackets end cell end table.

Latihan Bab

Konsep Kilat

Persamaan Trigonometri Dasar

Persamaan Trigonometri Lanjutan

Latihan Soal Persamaan Trigonometri

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Selesaikanlah persamaan berikut untuk 0 ∘ ≤ x ≤ 36 0 ∘ 4 cos 2 x ∘ + 3 sin 2 x ∘ = 3

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