Question

Let θ be an angle such that cot θ= 12/5 and secθ<0.
Find the exact values of cosθ and cscθ.

Answer 1

9514 1404 393

Answer:

cos(θ) = -12/13

csc(θ) = -13/5

Explanation:

The relation between the cot and csc is ...

cot² + 1 = csc²

The signs of the cot and sec tell you this is a 3rd quadrant angle, where cos and csc are both negative.

Then ...

csc(θ) = -√(1 +(12/5)²) = -√(169/25)

csc(θ) = -13/5

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cos(θ) = cot(θ)/csc(θ) = (12/5)/(-13/5)

cos(θ) = -12/13