Find the Exact Value arccos(-( square root of 3)/2)

Problem

arccos(−√(,3)/2)

Solution

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

2. Recall the unit circle values for the cosine function where cos(θ)=−√(,3)/2

3. Determine the angle in the second quadrant (since the value is negative) that corresponds to this coordinate.

4. Calculate the angle using the reference angle π/6 where cos(π/6)=√(,3)/2

5. Subtract the reference angle from π to find the value in the second quadrant.

π−π/6=(5*π)/6

Final Answer

arccos(−√(,3)/2)=(5*π)/6

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