Find the Exact Value arcsin(sin((3pi)/4))

Problem

arcsin(sin((3*π)/4))

Solution

1. Evaluate the inner trigonometric function sin((3*π)/4) Since (3*π)/4 is in the second quadrant, the sine value is positive.

sin((3*π)/4)=√(,2)/2

2. Substitute this value back into the inverse sine function.

arcsin(√(,2)/2)

3. Determine the angle θ such that sin(θ)=√(,2)/2 within the restricted range of the arcsine function, which is [−π/2,π/2]

θ=π/4

Final Answer

arcsin(sin((3*π)/4))=π/4

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