   Chapter 10, Problem 16PS

Chapter
Section
Textbook Problem

# Butterfly Curve Use a graphing utility to graph the curve shown in the figure below. The curve is given by r = e cos θ − 2 cos 4 θ + sin 5 θ 12 . Over what interval must θ vary to produce the curve? To determine

To graph: The polar curve r=ecosθ2cos4θ+sin5θ12 and determine the range of θ where the curve is identical to the one provided.

Explanation

Given: The graph:

Graph:

Use the Ti-83 calculator to sketch the graph:

Step 1: Press the [MODE] key and the select the Polar curve option.

Step 2: Press the [Y=] key and then enter the provided equation to the right of Y1.

Step 3: Press [WINDOW] and enter the following values

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