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

Problem

cos(arccos(3*π))

Solution

1. Identify the domain of the inverse cosine function, arccos(x)

2. Recall that the function y=arccos(x) is only defined for input values x in the interval [−1,1]

3. Compare the given input value 3*π to the domain boundaries.

4. Determine that since π≈3.14159 the value 3*π≈9.42477 which is significantly greater than 1

5. Conclude that because 3*π is outside the interval [−1,1] the expression arccos(3*π) is undefined in the set of real numbers.

Final Answer

cos(arccos(3*π))=Undefined

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