Chapter 4.6, Problem 37E

Solution

To graph : The function $y=\cos 3x-4\sin 2x$ showing one period.

Given information :

The function $y=\cos 3x-4\sin 2x$

Graph :

Consider the given function $y=\cos 3x-4\sin 2x$ .

Graph the given function in the viewing window $\left[-4\pi ,4\pi \right]$ by $\left[-6,6\right]$ .

  

From the graph it is evident that the curve repeats itself at the interval of $2\pi$ . Therefore, the graphical period is $2\pi$ .

Now, graph the given function showing one period in the viewing window $\left[-\pi ,\pi \right]$ by $\left[-6,6\right]$ .

  

Interpretation :

The period of the given function is $2\pi$ .