Q 35. - Calculus

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.

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

Step-by-Step Solution

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 1: Given information

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

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