SOLUTION: determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = -3 - 2cos(θ)

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Question 1137897: determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = -3 - 2cos(θ)
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
To see if a polar graph is symmetrical about the x-axis, substitute 2pi-theta for theta, then simplify.  If it can then be simplified
to the original equationb, then it is symmetrical about the x-axis.

To see if a polar graph is symmetrical about the y-axis, substitute pi-theta for theta, then simplify.  If it can then be simplified
to the original equationb, then it is symmetrical about the y-axis.

To see if a polar graph is symmetrical about the x-axis, substitute 2pi-theta for theta, then simplify.  If it can then be simplified
to the original equationb, then it is symmetrical about the x-axis.

To see if a polar graph is symmetrical about the origin, then you can 
proceed either of two ways:

1.  Show that it is symmetrical about both the x and y axes.

OR

2.  Substitute -r for r, then simplify.  If it can then be simplified
to the original equationb, then it is symmetrical about the origin.





Check for symmetry about the x-axis,





That's the same as the original equation, so it's symmetrical
about the x-axis.


Check for symmetry about the y-axis,







That's not same as the original equation, so it's not symmetrical
about the y-axis.


It's not symmetrical about both axes, so it's not symmetrical about the origin.

Edwin
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