Chapter EP, Problem 13.8.3EP

To determine

To find:The amplitude, period, graph and phase shift for the given function.

Answer to Problem 13.8.3EP

The amplitude, period, graph and phase shift for the given function is determined.

Explanation of Solution

Given:

$y=\tan \left(\theta +\frac{\pi }{2}\right)$

Calculation:

The general form of the phase shift is given as,

$\begin{array}{l}y=a\sin b\left(\theta -h\right)\\ y=a\cos b\left(\theta -h\right)\\ y=a\tan b\left(\theta -h\right)\end{array}$

If the value of h is greater than 0, then it shift towards the right

If the value of h is less than 0, then it shift towards the left.

Compare the given value with the general form.

The value of his $-\frac{\pi }{2}$ , then the graph shift towards the left.

The graph is plotted as,

From the graph the amplitude is infinite, the phase shift is $\frac{\pi }{2}$ .

Thus, the amplitude, period, graph and phase shift for the given function is determined.