   Chapter 10.3, Problem 48E

Chapter
Section
Textbook Problem

# The figure shows a graph of r as a function of θ in Cartesian coordinates. Use it to sketch the corresponding polar curve.48. To determine

To sketch: Polar curve from the given Cartesian curve shown below in figure 1.

Explanation

Given:

The polar curve is shown below in figure 1.

Calculation:

From the figure 1, when θ increases from 0 to π4 , polar curve r decreases from 2 to 1 in polar graph.

When θ increases from π4 to π2 , polar curve r increases from 1 to 2 .

When θ increases from π2 to 3π4 , polar curve r decreases from 2 to 1 .

When θ increases from 3π4 to π , polar curve r increases from 1 to 2 .

When θ increases from π to 5π4 , polar curve r decreases from 2 to 1

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