   Chapter 10.3, Problem 46E

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.46. r = cos(θ/3)

To determine

To sketch: The curves for the polar equation r=cos(θ3) and its Cartesian coordinates.

Explanation

Given:

The polar equation is as below.

r=cos(θ3) .

Calculation:

Substitute (0.0873) for θ in equation r=cos(θ3) .

r=cos(θ3)=cos((0)3)=1

For the polar equation r=cos(θ3) values for the Cartesian coordinates curve is tabulated below.

 θ (degrees) θ (rad) r 0 0 1 10 0.174611111 0.998306643 20 0.349222222 0.993232305 30 0.523833333 0.984794173 40 0.698444444 0.973020824

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

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