Question

Untuk x di kuadran 1 dan tan x = 2 - akar 3
hitunglah:
A. sin x
B. cos x

Answer 1

Tan α = 2 - √3 = y/x
r² = x² + y²
r² = 1 + (2-√3)² = 1 + 4 +3 - 4√3
r² = 8 - 4√3 = 8 - 2√12 = (√6 - √2)²
r = √6 - √2

sin α = y/r = (2 - √3)/(√6 - √2) = (2-√3)(√6+√2) / ( 4)
sin α = 1/4 ( 2-√3)(√6 +√2)

cos α = x/r = 1/ (√6- √2) = 1/4 (√6 - √2)