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.

$r=e^{\sin \theta }-2\cos 4\theta +{\sin }^5(\theta /12)$

Short answer

$[0,24\pi ]$

Step-by-step solution

Given information

$r=e^{\sin \theta }-2\cos 4\theta +{\sin }^5(\theta /12)$

Explanation

Consider the polar equation $r=e^{\sin \theta }-2\cos 4\theta +{\sin }^5\left(\frac{\theta }{12}\right)$

The goal is to draw the graph of the polar equation supplied. We will draw the graph here using a graphing calculator.

If we observe the graph, the values of the graph are repeated after an interval of $24\pi$so the smallest interval required for the graph is$[0,24\pi ]$Therefore, the smallest interval for the graph is $[0,24\pi ]$