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)

csc(y)=2

sin(y)=1/2

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

4. Recall from the unit circle or special triangles that sin(π/6)=1/2

Final Answer

arccsc(2)=π/6

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