Chapter 4.7, Problem 18E

a.

To determine

To complete: The given table using a graphing utility.

Explanation of Solution

Given Information: An incomplete table. Function is $y={\cos }^{-1}x$ .

Calculation:

  $\begin{array}{l}\begin{array}{llllll}x\hfill & -1\hfill & -0.8\hfill & -0.6\hfill & -0.4\hfill & -0.2\hfill \\ y\hfill & 3.14\hfill & 2.5\hfill & 2.21\hfill & 1.98\hfill & 1.77\hfill \end{array}\\ \\ \begin{array}{lllllll}x\hfill & 0\hfill & 0.2\hfill & 0.4\hfill & 0.6\hfill & 0.8\hfill & 1\hfill \\ y\hfill & 1.57\hfill & 1.37\hfill & 1.16\hfill & 0.93\hfill & 0.64\hfill & 0\hfill \end{array}\end{array}$

b.

To determine

To plot: The points from the table in previous part and graph the function.

Explanation of Solution

Given Information: A table from previous part.

Graph:

  

c.

To determine

To graph: The inverse cosine function using a graphing utility and then to compare the result with hand-drawn graph from previous part.

Answer to Problem 18E

Explanation of Solution

Given Information: Function is $y={\cos }^{-1}x$ .

Graph:

  

The graph is very much similar to the hand-drawn graph.

d.

To determine

To find: Any intercepts and symmetry of the graph.

Answer to Problem 18E

  $x-\mathrm{int}ercept$ is $(1,0)$ and $y-\mathrm{int}ercept$ is $(0,\frac{\pi }{2})$ , there is no symmetry.

Explanation of Solution

Given Information: Function is ${\cos }^{-1}x$ , graph from previous part.

  

From graph it can be observed that $y-\mathrm{int}ercept$ is $(0,\frac{\pi }{2})$ and $x-\mathrm{int}ercept$ is $(1,0)$ .

  $(0,\frac{\pi }{2})$ is on the graph but $(0,-\frac{\pi }{2})$ is not on graph,

  $\Rightarrow$ No symmetry about the $x-axis$ .

  $(1,0)$ is on the graph but $(-1,0)$ is not on graph,

  $\Rightarrow$ No symmetry about the $y-axis$ .

  $(-1,\pi )$ is on the graph but $(1,-\pi )$ is not on graph,

  $\Rightarrow$ No symmetry about the origin.

Thus, $x-\mathrm{int}ercept$ is $(1,0)$ and $y-\mathrm{int}ercept$ is $(0,\frac{\pi }{2})$ , there is no symmetry.