Find the Exact Value arcsin(( square root of 2)/2)

Problem

arcsin(√(,2)/2)

Solution

1. Identify the definition of the inverse sine function, which asks for an angle θ in the interval [−π/2,π/2] such that sin(θ)=√(,2)/2

2. Recall the unit circle values for common angles.

3. Determine the angle where the sine (the y-coordinate on the unit circle) is equal to √(,2)/2

4. Select the value θ=π/4 (or 45 because sin(π/4)=√(,2)/2 and π/4 falls within the required range [−π/2,π/2]

Final Answer

arcsin(√(,2)/2)=π/4

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