Q. 34. - 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.

$r=\frac{4\cos 3\theta +\cos 2\theta }{\cos \theta }$

Step-by-Step Solution

Answer

The interval is $\left[0,2\mathrm{\pi }\right]$.

The graph is as follows,

Step 1. Given Information.

The polar equation is $r=\frac{4\cos 3\theta +\cos 2\theta }{\cos \theta }$.

Step 2. Explanation.

Cosine is an even function and the graph in the polar plane will be symmetrical with respect to the horizontal axis. So the smallest interval to draw the graph is $\left[0,2\mathrm{\pi }\right]$.

Step 3 Graph.

The required graph is as follows,