Evaluate 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 within the interval [0,π]

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

4. Determine the angle in the second quadrant (where cosine is negative) by calculating π−(θ_ref)

5. Calculate the final value: π−π/3=(2*π)/3

Final Answer

arccos(−1/2)=(2*π)/3

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