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Chapter 13: Q. 10 (page 1026)

Explain how the symmetries of the graphs of polar functions can be used to simplify area calculations.

Short Answer

Expert verified

1. Substitute 胃for-胃. The graph is symmetric with respect to the polar axis if an equivalent equation is found.

2. Substitute 胃for-胃andrfor-r.The graph is symmetric with respect to 胃=蟺2if an equivalent equation is found.

3. Substitute -rforr.The graph is symmetric with respect to the pole if an analogous equation is found.

Step by step solution

01

Given Information

Given : Graphs of polar functions

02

Symmetry about the Origin

Symmetry about the origin :

If the equation remains unchanged when ris replaced by -r.

Example: r2=cos2胃

03

Symmetry about x-axis

Symmetry about x- axis :

If the equation remains unchanged when ris replaced by -r.

Example: r=cos3胃

04

Symmetry about y-axis

Symmetry about y-axis :

If the equation remains unchanged when 胃is replaced by 蟺-胃.

Example: r2=cos2胃

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