   Chapter 10.3, Problem 35E

Chapter
Section
Textbook Problem

Sketch the curve with the given polar equation by first sketching the graph of r as a function of θ in Cartesian coordinates.35. r = 3 cos 3θ

To determine

To sketch: The curve for the polar equation r=3cos3θ and its Cartesian coordinates.

Explanation

Calculation:

The polar equation is r=3cos3θ.

Substitute (0) for θ in equation r=3cos3θ,

r=3cos3θ=3cos3(0)=3

For the polar equation r=3cos3θ values for the Cartesian coordinates curve is tabulated below.

 θ r 0 3 π6 0 π3 −3 π2 0 2π3 3 5π6 0 π −3 7π6 0 4π3 3 3π2 0 5π3 −3 11π6 0 2π 3

The curve for the Cartesian coordinates is shown below in Figure 1.

From Figure 1, it is observed that when θ increases from 0 to π6, the polar curve r decreases from 3 to 0 in the polar graph.

It is observed that when θ increases from π6 to π3, the polar curve r decreases from 0 to 3

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