Find the Exact Value arcsin(3/8)

Problem

arcsin(3/8)

Solution

1. Identify the expression as an inverse trigonometric function, which represents the angle θ such that sin(θ)=3/8 within the restricted range [−π/2,π/2]

2. Check for standard values on the unit circle. The value 3/8 (or 0.375 does not correspond to the sine of any common reference angles such as 30 45 or 60

3. Determine if further simplification is possible. Since 3/8 is not a standard ratio and there are no other trigonometric functions applied to the expression, the exact value is written in its simplest form using the inverse sine notation.

Final Answer

arcsin(3/8)=arcsin(3/8)

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