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Graph the equation in the θr-plane. Label each arc of your curve with the quadrant in which the corresponding polar graph will occur.

r=cos2θ

Short Answer

Expert verified

The graph of the equation:

Step by step solution

01

Step 1. Given information

The equation of the curve:

r=cos2θ

02

Step 2. Simplify the equation:

The function can be simplified as:

r=cos2θr=1+cos2θ2r=12+12cos2θ

03

Step 3. Graph the equation in θr-plane. 

The value of θlies on the horizontal axis and rlies on the vertical axis.

The graph of r=12+12cos2θ is obtained by compressing the the graph of r=cosθby factor of 12horizontally then compress the graph vertcally by a factor of 12then vertcally shift the graph by 12units upward.

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