Find the Exact Value arccos(pi/3)

Problem

arccos(π/3)

Solution

1. Identify the domain of the inverse cosine function. The function y=arccos(x) is defined only for values of x in the interval [−1,1]

2. Compare the given input value to the domain boundaries. The value π is approximately 3.14159

3. Calculate the approximate value of the fraction.

π/3≈3.14159/3≈1.047

4. Determine if the value is within the valid range. Since 1.047>1 the value π/3 lies outside the domain [−1,1]

5. Conclude that the expression does not have a real value.

Final Answer

arccos(π/3)=Undefined

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