Question

Diketahui sin 5°=x dan cos 5°=y maka sin 40° = .... tolong bantuin mas mba terima kasih

Answer 1

Misal A= 5°
40° = 8A

sin 40° = sin 8A
sin 8A = sin 2(4A) = 2 sin 4A cos 4A

sin 4A = 4 sin A cos A - 8 sin³ A cos A 
sin 4A = 4 x y - 8x³ y

cos 4A = 8 cos⁴ A - 8 cos² A + 1
cos 4A = 8y⁴ - 8y² + 1
.
sin 8A = 2( 4xy -8x³y)(8y⁴-8y²+1)
sin 8A = (8xy -16x³y)(8y⁴-8y²+1)
sin 8A = 64 x⁴y⁴ -108 x³y⁵ -64 xy³ + 108 x³y³ + 8xy -16x³y