POSSIBLE POINTS: Find cott given that cost =
and cott < 0. Show all algebraic work to support your answer.
Please quickly

Recall that

cos²(x) + sin²(x) = 1

for any x. Also, remember that cotangent is defined as

cot(x) = cos(x) / sin(x)

We're given that cos(t ) = 5/13 and cot(t ) < 0, which means sin(t ) must be negative. So when we solve for sin(t ) in the first relation, we have to take the negative square root:

sin²(t ) = 1 - cos²(t )

sin(t ) = -√(1 - cos²(t ))

sin(t ) = -√(1 - (5/13)²) = -12/13

Then

cot(t ) = (5/13) / (-12/13) = -5/12