Chapter 14.7, Problem 28WE

To determine

To Find: The graph for the given expression without the use of trigonometric or inverse trigonometric functions.

Answer to Problem 28WE

The required graph is shown in Figure 1

Explanation of Solution

Given:

The given expression is $y={\csc }^{-1}x$ .

Calculation:

Consider the given expression is,

  $y={\sec }^{-1}x$

Rewrite the above expression as,

  $x=\csc y$

The table for the value of $y$ for different value of $x$ is shown in Table 1

Table 1

$y$	$x=\csc y$
0	Undefined
$\frac{\pi }{4}$	1.414
$\frac{\pi }{2}$	1
$\pi$	undefined

The graph for the function with the help of the points is shown in Figure 1

  

Figure 1