Find the Exact Value sin(arccos(1/2))

Problem

sin(arccos(1/2))

Solution

1. Identify the inner value θ=arccos(1/2) This means we are looking for an angle θ in the interval [0,π] such that cos(θ)=1/2

2. Determine the angle θ from the unit circle. Since cos(π/3)=1/2 we have θ=π/3

3. Substitute the angle back into the outer function to find sin(π/3)

4. Evaluate the sine of the angle using known trigonometric values.

sin(π/3)=√(,3)/2

Final Answer

sin(arccos(1/2))=√(,3)/2

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