Simplify arcsin( square root of 2/2)

Problem

arcsin(√(,2)/2)

Solution

1. Identify the goal, which is to find an angle θ in the restricted range of the inverse sine function, [−π/2,π/2] such that sin(θ)=√(,2)/2

2. Recall the unit circle values for the sine function.

3. Determine that the sine of π/4 (or 45 is equal to √(,2)/2

4. Verify that π/4 falls within the interval [−π/2,π/2]

Final Answer

arcsin(√(,2)/2)=π/4

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