Chapter 4.7, Problem 122E

To determine

To approximate: the value of the expression.

Answer to Problem 122E

The value of the expression 2.29.

Explanation of Solution

Given information:

Given expression

  $\mathrm{arcsec}\left(-1.52\right)$ .

Calculation:

Find out the approximate value of the expression $\mathrm{arcsec}\left(-1.52\right)$ with the help of a calculator. The graph for this function is as shown below.

  

If $y=\mathrm{arcsec}x$ then its range is $0\le y\le \pi ,y\ne \frac{\pi }{2}$ and domain is $\left|x\right|\ge 1$ .

Hence $-1.52$ lies in the domain of the $\mathrm{arcsec}$ function.

Now that we have checked the functions domain, we will proceed to find the value of this expression.

From the graphing calculator Maple, we can get this value by typing in the following code.

  $\begin{array}{c}>\mathrm{arcsec}\left(-1.52\right)\\ 2.28881623\end{array}$

Hence, $\mathrm{arcsec}\left(-1.52\right)=2.29$ .