Find the Exact Value arccos(cos((7pi)/6))

Problem

arccos(cos((7*π)/6))

Solution

1. Evaluate the inner cosine function. The angle (7*π)/6 is in the third quadrant, where the cosine value is negative.

cos((7*π)/6)=−√(,3)/2

2. Identify the range of the inverse cosine function. The principal value range for arccos(x) is [0,π]

3. Find the angle θ in the interval [0,π] such that cos(θ)=−√(,3)/2 Since the value is negative, the angle must be in the second quadrant.

θ=π−π/6

4. Simplify the expression to find the final angle.

θ=(5*π)/6

Final Answer

arccos(cos((7*π)/6))=(5*π)/6

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