Find csc θ if cot θ = −21/20 and sin θ > 0.

Note the answer must be positive because if sin>0, then csc > 0.
There are two ways to do this problem.
1) Use a trig identity:

Sub in value for cot


2) Use a right triangle and SOH CAH TOA
cot = 1/tan = adjacent/opposite = -21/20
Therefore adjacent side = 21, opposite side = 20
Use pythagorean thm to find hypotenuse:


csc = 1/sin = hypotenuse/opposite = 29/20

Hope this helps.