Find the Exact Value sec(arcsec(1/2))

Problem

sec(arcsec(1/2))

Solution

1. Identify the domain of the inverse secant function, arcsec(x)

2. Recall that the domain of arcsec(x) is (−∞,−1]∪[1,∞)

3. Evaluate the input value x=1/2 against the domain.

4. Determine that since |1/2|<1 the value 1/2 is not in the domain of the inverse secant function.

5. Conclude that the expression is undefined because the inner function cannot be evaluated for this input.

Final Answer

sec(arcsec(1/2))=undefined

Want more problems? Check here!