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): You can put this solution on YOUR website!
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): You can put this solution on YOUR website!
in Quadrant II
which is to say:
In Quadrant II, \ \geq\ 0)
and \ \leq\ 0)
\ =\ \frac{1}{\sin(\varphi))
Hence
\ =\ 2)
and \ =\ \frac{1}{2})
Furthermore:
\ =\ \sqrt{1\ -\ \sin^2(\varphi)})
So
\ =\ \frac{1}{2}\ \Rightarrow\ \cos(t)\ =\ \pm\frac{\sqrt{3}}{2})
But for Quadrant II so we need \ =\ -\frac{\sqrt{3}}{2})
Next:
\ =\ \frac{\cos(\varphi)}{\sin(\varphi)})
Hence:
\ =\ \frac{\frac{-\sqrt{3}}{2}}{\frac{1}{2}}\ =\ -\sqrt{3})
John
My calculator said it, I believe it, that settles it
Answer by jrfrunner(365) (Show Source): You can put this solution on YOUR website!
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)
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