if cos 0= 0.5 find csc (0- pi/2)

Answer 1

cosθ = 1/2
make a sketch of the corresponding triangle, x=1, r=2
x^2 + y^2 = r^2
y^2 = 3
y = ±√3
so sinθ = √3/2 in quadrant I and sinθ = -θ 3/2 in quad IV

sin(θ -π/2) = -sin(π/2 - θ) = -cosθ , because of the complementary angle property
thus csc(θ - π/2) = - secθ = -2

or, even simpler

since cosθ = .5 , θ = 60°
csc(60-90)
= csc(-30°)
= -csc(30°) = -1/(1/2) = -2