Chapter 1.6, Problem 62E

To determine

To graph: The one possible period of the given function by graphical calculator.

Explanation of Solution

Given information: The given function is $f\left(x\right)=\cos \left(60\pi x\right)$ .

Graph:

Consider the function $f\left(x\right)=\cos \left(60\pi x\right)$ . It is known that the period of $\sin x$ is $2\pi$ . So, the period of given function is:

  $\frac{2\pi }{60\pi }=\frac{1}{30}$

First press “ON” button on graphical calculator, press $\boxed{\text{Y}=}$ key and enter right hand side of the equation $f\left(x\right)=\cos \left(60\pi x\right)$ after the symbol ${\text{Y}}_1$ . Enter the keystrokes $\boxed{\text{COS}}\boxed{60}\boxed{\text{2nd}}\boxed{\wedge }\boxed{\text{X}}\boxed{)}$ .

The display will show the equation,

  ${\text{Y}}_{\text{1}}=\cos \left(60\pi \text{X}\right)$

Set the window at $\left[-\frac{1}{60},\frac{1}{60}\right]$ by $\left[-2,2\right]$ . Now, press the $\boxed{\text{GRAPH}}$ key and $\boxed{\text{TRACE}}$ key to produce the graph of given quadratic equation in standard window as shown below.

  

Figure (1)

Interpretation: From the above it can be observed that the graph represents a periodicity after $\frac{1}{30}$ .