SOLUTION: Use the given information to determine the exact trigonometric value. Find csc(theta) if cot(theta) =-8 and 3pi/2 < theta < 2pi

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Question 1031102: Use the given information to determine the exact trigonometric value.
Find csc(theta) if cot(theta) =-8 and 3pi/2 < theta < 2pi
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


means

In QIV, , so and are negative as well.



So if then

Square both sides:



Substitute from the Pythagorean Identity:







in general, but recall the restriction to QIV, hence



Then, since cosecant is the reciprocal of sine:



John

My calculator said it, I believe it, that settles it