Find the Exact Value tan(arctan(4))

Problem

tan(arctan(4))

Solution

1. Identify the relationship between the tangent function and its inverse, the arctangent function.

2. Apply the property of inverse functions, which states that ƒ*(ƒ(x)(−1))=x for all x in the domain of the inverse function.

3. Determine the domain of the arctangent function, which is all real numbers (−∞,∞)

4. Evaluate the expression since 4 is within the domain of the arctangent function, meaning the functions cancel each other out.

Final Answer

tan(arctan(4))=4

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