Find csc theta, given that cot theta =-1/2 and theta is in quadrent IV

Answer 1

cotθ = -1/2 or tanθ = -2/1
sketch the triangle in standard position, so
x^2 + y^2 = r^2
r^2 = 1 + 4 = 5
r = √5

if θ is in quad IV, x = 1, y = -2, r = √5
sinθ = y/r = -2/√5
cscθ = - √5/2