Assume that the range of f(x) = arccsc(x) is [0, pi/2) U [p, 3pi/2) when finding the exact value of the following of arccsc(-2) in radical fraction form.

Question

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Answer 1

If y = arccsc(-2), then cscy = -2 and y is in the range of arccscx.  

 

So, since cscy < 0, and y is either in quadrant 1 or 3, we can conclude that y lies in quadrant 3.  

 

cscy = 1/siny = -2

 

siny = -1/2 and π ≤ y ≤ 3π/2

 

    y = 7π/6