Find the Value Using the Unit Circle arccos(-1/2)

Problem

arccos(−1/2)

Solution

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

2. Determine the angle θ in the interval [0,π] such that cos(θ)=−1/2

3. Locate the point on the unit circle where the xcoordinate is −1/2 within the upper half of the circle (Quadrants I and II).

4. Recognize that the reference angle for which cos((θ_ref))=1/2 is π/3

5. Calculate the angle in Quadrant II by subtracting the reference angle from π π−π/3=(2*π)/3

Final Answer

arccos(−1/2)=(2*π)/3

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