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Selesaikanlah persamaan berikut untuk 0 ∘ ≤ x ≤ 36 0 ∘ 5 cos x ∘ − 12 sin x ∘ = 13

Selesaikanlah persamaan berikut untuk 

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02

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22

:

33

:

36

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Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

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 5 cos space x minus 12 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 5 row cell k sin space alpha degree end cell equals 12 row k equals cell square root of 12 squared plus 5 squared end root end cell row blank equals cell square root of 144 plus 25 end root end cell row blank equals cell square root of 169 end cell row blank equals 13 row cell tan space alpha degree end cell equals cell 12 over 5 space left parenthesis kuadran space straight I right parenthesis end cell row cell alpha degree end cell equals cell 67 comma 38 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 13 cos space left parenthesis x plus 67 comma 38 right parenthesis degree equals 13 end cell row blank left right double arrow cell cos space left parenthesis x plus 67 comma 38 right parenthesis degree equals 1 end cell end table

table attributes columnalign right center left columnspacing 0px end attributes row cell cos space left parenthesis x plus 67 comma 38 right parenthesis degree end cell equals 1 row cell cos space left parenthesis x plus 67 comma 38 right parenthesis degree end cell equals cell cos space 0 degree end cell row cell space x plus 67 comma 38 degree end cell equals cell 0 degree plus n times 360 degree end cell row x equals cell negative 67 comma 38 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 67 comma 38 degree plus 0 times 360 degree end cell row blank equals cell negative 67 comma 38 degree end cell row x equals cell negative 67 comma 38 degree plus 1 times 360 degree end cell row blank equals cell 292 comma 62 degree end cell end table

Dengan demikian,

table attributes columnalign right center left columnspacing 0px end attributes row HP equals cell open curly brackets 292 comma 62 degree close curly brackets end cell end table.

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