Find the Exact Value arcsin(15/17)

Problem

arcsin(15/17)

Solution

1. Identify the expression as an inverse trigonometric function, which represents an angle θ such that sin(θ)=15/17

2. Determine if the value 15/17 corresponds to a standard angle on the unit circle (like 30 45 or 60.

3. Conclude that since 15/17 is not a standard ratio, the exact value is expressed in its simplest form as the inverse sine function itself.

4. Approximate the value if needed for context, noting that θ≈1.0808 radians or θ≈61.93 but the exact mathematical expression remains unchanged.

Final Answer

arcsin(15/17)=arcsin(15/17)

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