Find the Exact Value arccsc(-2)

Problem

arccsc(−2)

Solution

1. Identify the definition of the inverse cosecant function, where y=arccsc(x) means csc(y)=x for y in the range [−π/2,0)∪(0,π/2]

2. Rewrite the expression in terms of the sine function using the reciprocal identity csc(y)=1/sin(y)

sin(y)=1/(−2)

3. Determine the angle y in the interval [−π/2,π/2] such that sin(y)=−1/2

4. Recall the unit circle values where sin(−π/6)=−1/2

5. Verify that −π/6 falls within the restricted range of the arccosecant function.

Final Answer

arccsc(−2)=−π/6

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