Find the Exact Value arcsin(0.635)

Problem

arcsin(0.635)

Solution

1. Identify the expression as the inverse sine function, which asks for the angle θ such that sin(θ)=0.635 within the range [−π/2,π/2]

2. Recognize that 0.635 is not a standard value from the unit circle (like 0.5 or √(,2)/2, so the exact value is represented by the expression itself or its decimal approximation.

3. Calculate the numerical value using a calculator to provide the result in radians.

4. Approximate the value to several decimal places.

Final Answer

arcsin(0.635)≈0.68808

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