SOLUTION: what is the exact value of csc(tan^-1(-0.62))

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Question 708067: what is the exact value of
csc(tan^-1(-0.62))
Answer by Edwin Parker(36) About Me  (Show Source):
You can put this solution on YOUR website!
csc[tan-1(-0.62)]

The inverse tangent of a negative number is a negative angle
in the fourth quadrant.  The cosecant of an angle in the fourth 
quadrant is negative.  So the answer will be negative.

Let ϴ = tan-1(-0.62)

Then  

csc[tan-1(-0.62)] = csc(ϴ) 

So we want csc(ϴ)

tan(ϴ) = -0.62 = -62%2F100 = -31%2F50

cot(ϴ) = 1%2Ftan%28theta%29 = -50%2F31

We use 

cscē(ϴ) = 1 + cotē(ϴ) 

cscē(ϴ) = 1 + %28-50%2F31%29%5E2

cscē(ϴ) = 1 + 2500%2F961

cscē(ϴ) = 961%2F961 + 2500%2F961

cscē(ϴ) = 3461%2F961

Take square roots of both sides.  And since we know
the answer is negative, we take the negative square root:

 csc(ϴ) = -sqrt%283461%2F961%29

 csc(ϴ) = -sqrt%283461%29%2F31%29

Edwin