Question

Find the smallest interval necessary to draw a complete graph of the functions in Exercises $33–38$and then graph each function using a graphing calculator or computer algebra system.

$r=\frac{4\cos \theta +\cos 9\theta }{\cos \theta }$

Short answer

$\left[0,\frac{\pi }{2}\right)\cup \left(\frac{\pi }{2},\frac{3\pi }{2}\right)\cup \left(\frac{3\pi }{2},2\pi \right]$

Step-by-step solution

Given information

$r=\frac{4\cos \theta +\cos 9\theta }{\cos \theta }$

Explanation

Consider the polar equation $r=\frac{4\cos \theta +\cos 9\theta }{\cos \theta }$ The goal is to draw the graph of the polar equation supplied.

We will draw the graph here using a graphing calculator.

If we look at the graph, we can see that it repeats itself over a period of time. $\left[0,\frac{\pi }{2}\right)\cup \left(\frac{\pi }{2},\frac{3\pi }{2}\right)\cup \left(\frac{3\pi }{2},2\pi \right]$Therefore, the answer is $\left[0,\frac{\pi }{2}\right)\cup \left(\frac{\pi }{2},\frac{3\pi }{2}\right)\cup \left(\frac{3\pi }{2},2\pi \right]$