Chapter SH, Problem 12.21EP

To determine

To find: The amplitude, period, phase shift, and vertical shift for each function. And then graph the function.

Answer to Problem 12.21EP

The amplitude of the given function is $4$ ,the period is $2\pi$ and phase shift is $\frac{\pi }{2}$ and the vertical shift is $2$ and the graph is shown below.

Explanation of Solution

Given:

The given function is:

  $y=4\cos \left(\theta -\frac{\pi }{2}\right)-2$ .

Consider the cosine function:

  $y=A\cos \left(B\left(x-C\right)\right)+D$

The amplitude and period of the tangent function is given as:

The amplitude is $A$ .

The period of tangent function is $\frac{2\pi }{B}$ .

The vertical shift is $D$ .

The phase shift is $\frac{C}{B}$ .

The amplitude of the given function is $4$ .

The period is $2\pi$ .

The phase shift is $\frac{\pi }{2}$ .

The vertical shift is $2$ .

The graph of the given function is as:

  

Therefore the amplitude of the given function is $4$ ,the period is $2\pi$ and phase shift is $\frac{\pi }{2}$ and the vertical shift is $2$ and the graph is shown above.