Find the Exact Value arcsin(cos(pi/2))

Problem

arcsin(cos(π/2))

Solution

1. Evaluate the inner trigonometric function cos(π/2)

2. Recall that on the unit circle, the cosine of π/2 radians (90 is 0

cos(π/2)=0

3. Substitute this value back into the original expression.

arcsin(0)

4. Determine the angle θ in the restricted range of the inverse sine function, [−π/2,π/2] such that sin(θ)=0

5. Identify that sin(0)=0 which falls within the required range.

arcsin(0)=0

Final Answer

arcsin(cos(π/2))=0

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