Find the Exact Value arccos(-1/2)

Problem

arccos(−1/2)

Solution

1. Identify the range of the inverse cosine function, which is [0,π]

2. Set the expression equal to an angle θ such that cos(θ)=−1/2 where 0≤θ≤π

3. Determine the reference angle in the first quadrant where cos((θ_ref))=1/2 which is π/3

4. Locate the angle in the second quadrant because the cosine value is negative and the range is [0,π]

5. Calculate the angle using the formula θ=π−(θ_ref)

6. Simplify the expression π−π/3 to find the final value.

Final Answer

arccos(−1/2)=(2*π)/3

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