Chapter 4.7, Problem 132E

To determine

To approximate: the value of the expression.

Answer to Problem 132E

The value of the expression $-0.41$ .

Explanation of Solution

Given information:

Given expression

  $\mathrm{arccot}\left(-\frac{16}{7}\right)$ .

Calculation:

Find out the approximate value of the expression $\mathrm{arccot}\left(-\frac{16}{7}\right)$ with the help of a calculator. The graph for this function is as shown below.

  

  $y=\mathrm{arccot}x$ then its range is $0<y<\pi ,$ and domain is $-\infty <x<\infty$ .

Hence $-\frac{16}{7}$ lies in the domain of the $\mathrm{arccot}$ function.

Now, to find the value of this expression.

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

  $\begin{array}{c}>\mathrm{arccot}\left(\frac{16}{7}\right)\\ \underrightarrow{\text{at}\text{5}\text{digits}}0.41241\end{array}$

Hence $\mathrm{arccot}\left(-\frac{16}{7}\right)=-0.41$ .