Question

1. hitunglah nilai dari :
a. sin 112,5°
b. cos 75°

Answer 1

1) cos 2A = 1 - 2sin^2 A
Cos 225 = cos 2(112,5)
-1/2 √2 = 1 - 2 sin^2 112,5
2 sin^2 112,5 = 1 + 1/2 √2
sin^2 112,5 = 1/2 + 1/4 √2
(sin 112,5)^2 = (2 + √2)/4
Sin 112,5 = 1/2 √(2 + √2)

Cos 75 = cos (45 + 30)
= Cos 45 cos 30 - sin 45 sin 30
= 1/2 √2 . 1/2 √3 - 1/2 √2 . 1/2
= 1/4 √6 - 1/4 √2
= 1/4 (√6 - √2) atau 1/4 √2 (√3 - 1)