SOLUTION: If cot t=1/3, and &#960; < t < 3&#960;/2, what is the value of sin t.

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Question 333079: If cot t=1/3, and π < t < 3π/2, what is the value of sin t.
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
cot(t) =1/3 is the same as tan(t)=3
therefore
tan(t)=3 can be solved as t= Arctan(3)=71.565-/+n*180 (note 71.565 is in quadrant I and you want to be in quadrant III)
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since the domain is restricted to π < t < 3π/2
This puts you in quadrant III where both x and y are negative.
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so the answer is
t= Arctan(3)=71.565-/+180=251.565 (or -108.435)