Question 1137897
<pre>
To see if a polar graph is symmetrical about the x-axis, substitute <font face="symbol">2pi</font>-<font face="symbol">theta</font> for <font face="symbol">theta</font>, 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 <font face="symbol">pi</font>-<font face="symbol">theta</font> for <font face="symbol">theta</font>, 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 <font face="symbol">2pi</font>-<font face="symbol">theta</font> for <font face="symbol">theta</font>, 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(theta)}}}

{{{r = -3 - 2cos(2pi-theta)}}}

Check for symmetry about the x-axis,

{{{r = -3 - 2cos(2pi - theta)}}}

{{{r = -3 - 2cos(theta)}}}

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(pi - theta)}}}

{{{r = -3 - 2(-cos(theta)^"")}}}

{{{r = -3 + 2cos(theta)}}}

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</pre>