Simplify sin(arccos(( square root of 3)/2))

Problem

sin(arccos(√(,3)/2))

Solution

1. Evaluate the inner inverse trigonometric function by finding the angle θ such that cos(θ)=√(,3)/2 within the restricted range [0,π]

2. Identify the angle from the unit circle where the cosine value is √(,3)/2 which is θ=π/6 (or 30.

3. Substitute this angle back into the outer sine function to get sin(π/6)

4. Calculate the sine of π/6 using the unit circle or standard trigonometric values.

Final Answer

sin(arccos(√(,3)/2))=1/2

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