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

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


   

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(20064) About Me  (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.

r+=+-3+-+2cos%28theta%29

r+=+-3+-+2cos%282pi-theta%29

Check for symmetry about the x-axis,

r+=+-3+-+2cos%282pi+-+theta%29

r+=+-3+-+2cos%28theta%29

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


Check for symmetry about the y-axis,

r+=+-3+-+2cos%28pi+-+theta%29

r+=+-3+-+2%28-cos%28theta%29%5E%22%22%29

r+=+-3+%2B+2cos%28theta%29

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