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.

$r=e^{\sin \theta }-2\cos 4\theta$

Short answer

$[0,2\pi ]$

Step-by-step solution

Given information

$r=e^{\sin \theta }-2\cos 4\theta$

Explanation

Consider the polar equation $r=e^{\sin \theta }-2\cos 4\theta$

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, it repeats after an interval of $2\pi$so the smallest interval required for the graph is $[0,2\pi ]$

Therefore, the smallest interval for the graph is $[0,2\pi ]$