Simplify 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 which occurs at θ=π/6

3. Apply the property for negative arguments of the inverse cosine function, arccos(−x)=π−arccos(x)

4. Substitute the known value into the property: π−π/6

5. Simplify the expression by finding a common denominator to subtract the fractions.

Final Answer

arccos(−√(,3)/2)=(5*π)/6

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