Pertanyaan

Nilai dari sin 4 0 ∘ − sin 8 0 ∘ + sin 2 0 ∘ adalah ....

Nilai dari $sin 4 0^{\circ} - sin 8 0^{\circ} + sin 2 0^{\circ}$ adalah ....

N. Putri

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Ingat kembali identitas-identitas trigonometri berikut! Dengan demikian, didapat perhitungan sebagai berikut. Karena , maka didapat hasil sebagai berikut. Jadi, jawaban yang tepat adalah C.

Ingat kembali identitas-identitas trigonometri berikut!

$begin mathsize 14px style sin invisible function application straight alpha plus sin invisible function application straight beta equals 2 space sin invisible function application open parentheses fraction numerator straight alpha plus straight beta over denominator 2 end fraction close parentheses cos invisible function application open parentheses fraction numerator straight alpha minus straight beta over denominator 2 end fraction close parentheses sin invisible function application straight alpha minus sin invisible function application straight beta equals 2 space cos invisible function application open parentheses fraction numerator straight alpha plus straight beta over denominator 2 end fraction close parentheses sin invisible function application open parentheses fraction numerator straight alpha minus straight beta over denominator 2 end fraction close parentheses end style$

Dengan demikian, didapat perhitungan sebagai berikut.

$begin mathsize 14px style sin invisible function application 40 degree minus sin invisible function application 80 degree plus sin invisible function application 20 degree equals left parenthesis sin invisible function application 40 degree minus sin invisible function application 80 degree space right parenthesis plus sin invisible function application 20 degree space equals 2 space cos invisible function application open parentheses fraction numerator 40 degree plus 80 degree over denominator 2 end fraction close parentheses sin invisible function application open parentheses fraction numerator 40 degree minus 80 degree over denominator 2 end fraction close parentheses plus sin invisible function application 20 degree space equals 2 space cos invisible function application open parentheses fraction numerator 120 degree over denominator 2 end fraction close parentheses space sin invisible function application open parentheses fraction numerator negative 40 degree over denominator 2 end fraction close parentheses plus sin invisible function application 20 degree space equals 2 space cos invisible function application 60 degree space sin invisible function application left parenthesis negative 20 degree right parenthesis plus sin invisible function application 20 degree equals 2 times 1 half times sin invisible function application left parenthesis negative 20 degree right parenthesis plus sin invisible function application 20 degree equals sin invisible function application left parenthesis negative 20 degree right parenthesis plus sin invisible function application 20 degree end style$

Karena sin left parenthesis negative x right parenthesis equals negative sin x , maka didapat hasil sebagai berikut.

Jadi, jawaban yang tepat adalah C.