Find the Exact Value arcsin(cos(pi/4))

Problem

arcsin(cos(π/4))

Solution

1. Evaluate the inner trigonometric function cos(π/4) using the unit circle or special right triangles.

cos(π/4)=√(,2)/2

2. Substitute the value back into the original expression.

arcsin(√(,2)/2)

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

sin(π/4)=√(,2)/2

4. Conclude that the value of the inverse sine function is the angle found in the previous step.

arcsin(√(,2)/2)=π/4

Final Answer

arcsin(cos(π/4))=π/4

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