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Pertanyaan

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

Selesaikanlah persamaan berikut untuk 

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Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

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 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 3 row cell k sin space alpha degree end cell equals 1 row k equals cell square root of 3 squared plus 1 squared end root end cell row blank equals cell square root of 9 plus 1 end root end cell row blank equals cell square root of 10 end cell row cell tan space alpha degree end cell equals cell 1 third space left parenthesis kuadran space straight I right parenthesis end cell row cell alpha degree end cell equals cell 18 comma 43 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 10 cos space left parenthesis x plus 18 comma 43 right parenthesis degree equals square root of 3 end cell row blank left right double arrow cell cos space left parenthesis x plus 18 comma 43 right parenthesis degree equals fraction numerator square root of 3 over denominator square root of 10 end fraction end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space left parenthesis x plus 18 comma 43 right parenthesis degree end cell equals cell fraction numerator square root of 3 over denominator square root of 10 end fraction end cell row cell cos space left parenthesis x plus 18 comma 43 right parenthesis degree end cell equals cell cos space 56 comma 79 degree end cell row cell space x plus 18 comma 43 degree end cell equals cell plus-or-minus 56 comma 79 degree plus n times 360 degree end cell row x equals cell 38 comma 36 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 38 comma 36 degree plus 0 times 360 degree end cell row blank equals cell 38 comma 36 degree end cell row x equals cell 38 comma 36 degree plus 1 times 360 degree end cell row blank equals cell 398 comma 36 degree end cell row cell atau space x end cell equals cell negative 75 comma 22 degree plus n times 360 degree end cell row n equals cell 0 comma space 1 end cell row x equals cell negative 75 comma 22 degree plus 0 times 360 degree end cell row blank equals cell negative 75 comma 22 degree end cell row x equals cell negative 75 comma 22 degree plus 1 times 360 degree end cell row blank equals cell 284 comma 78 degree end cell end table

Dengan demikian,

table attributes columnalign right center left columnspacing 0px end attributes row HP equals cell open curly brackets 38 comma 36 degree comma space 284 comma 78 degree close curly brackets end cell end table.

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