SOLUTION: if t is in quadrant II and csc t=2, find the value of cot t.

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Question 334138: if t is in quadrant II and csc t=2, find the value of cot t.
Found 3 solutions by Alan3354, solver91311, jrfrunner:
Answer by Alan3354(69443)   (Show Source):
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if t is in quadrant II and csc t=2, find the value of cot t.
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If csc(t) = 2, sin(t) = 1/2.
arcsin(1/2) = 150 degs in Quad II.
cot(150) = - sqrt(3)

Answer by solver91311(24713)   (Show Source):
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in Quadrant II

which is to say:

In Quadrant II, and

Hence

and

Furthermore:

So

But for Quadrant II so we need

Next:

Hence:

John

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

Answer by jrfrunner(365)   (Show Source):
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Quadrant II is where x=cost is negative and y=sint is positive
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csc(t) = 2; 1/sin(t)=2; sin(t)=1/2 therefore t=30 (actually 180-30=150)
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Cot(t)=cos(t)/sin(t)
cot(150)=cos(150)/sin(150) = -cos(30)/sin(30)=(-sqrt(3)/2)/(1/2)=-sqrt(3)