Q 36. - 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.

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

Step-by-Step Solution

Answer

$[0,2\pi ]$

Step 1: Given information

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

Step 2: 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 $[0,2\pi ]$