Find the Exact Value arccos(cos((4pi)/3))

Problem

arccos(cos((4*π)/3))

Solution

1. Evaluate the inner cosine function cos((4*π)/3) Since (4*π)/3 is in the third quadrant, the cosine value is negative.

cos((4*π)/3)=−1/2

2. Identify the range of the inverse cosine function arccos(x) which is [0,π]

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

θ=(2*π)/3

Final Answer

arccos(cos((4*π)/3))=(2*π)/3

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