Pertanyaan

sin 15 0 ∘ cos 22 5 ∘ sin 27 0 ∘ cos 13 5 ∘ tan 13 5 ∘ = ...

$\frac{sin 27 0 ^{\circ} cos 13 5 ^{\circ} tan 13 5 ^{\circ}}{sin 15 0 ^{\circ} cos 22 5 ^{\circ}} = ...$

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Klaim

S. Nur

Master Teacher

Jawaban terverifikasi

Jawaban

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$fraction numerator sin 270 degree space cos 135 degree space tan 135 degree over denominator sin 150 degree cos 225 degree end fraction equals 2$ .

Pembahasan

Kita ingat sudut berelasi di kuadranII dan kuadran III, serta ingat nilai trigonometri untuk sudut istimewa, Jadi, .

Kita ingat sudut berelasi di kuadran II dan kuadran III, serta ingat nilai trigonometri untuk sudut istimewa,

$fraction numerator sin 270 degree space cos 135 degree space tan 135 degree over denominator sin 150 degree cos 225 degree end fraction equals fraction numerator sin open parentheses 180 degree plus 90 degree close parentheses space cos open parentheses 180 degree minus 45 degree close parentheses space tan open parentheses 180 degree minus 45 degree close parentheses over denominator sin open parentheses 180 degree minus 30 degree close parentheses space cos open parentheses 180 degree plus 45 degree close parentheses end fraction equals fraction numerator negative sin 90 degree space open parentheses negative cos 45 degree close parentheses space open parentheses negative tan 45 degree close parentheses over denominator sin 30 degree space open parentheses negative cos 45 degree close parentheses end fraction equals fraction numerator open parentheses negative 1 close parentheses space. space open parentheses negative begin display style 1 half end style square root of 2 close parentheses space. space open parentheses negative 1 close parentheses over denominator begin display style 1 half end style space. space open parentheses negative begin display style 1 half end style square root of 2 close parentheses end fraction equals 2$

Jadi, $fraction numerator sin 270 degree space cos 135 degree space tan 135 degree over denominator sin 150 degree cos 225 degree end fraction equals 2$ .