Question

Given sinθ = 2/5 and cosθ < 0: 1. Find cscθ 2. Find cotθ

Answer 1

Recall that

sin²(θ) + cos²(θ) = 1

for all θ, and given that cos(θ) < 0, we find that

cos(θ) = -√(1 - sin²(θ)) = -√(1 - (2/5)²) = -√(21)/5

Now,

csc(θ) = 1/sin(θ) = 1/(2/5) = 5/2

and

cot(θ) = cos(θ)/sin(θ) = (-√(21)/5)/(2/5) = -√(21)/2