document.write( "Question 1137897: determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
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Algebra.Com's Answer #755759 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "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\r\n" );
document.write( "to the original equationb, then it is symmetrical about the x-axis.\r\n" );
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document.write( "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\r\n" );
document.write( "to the original equationb, then it is symmetrical about the y-axis.\r\n" );
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document.write( "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\r\n" );
document.write( "to the original equationb, then it is symmetrical about the x-axis.\r\n" );
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document.write( "To see if a polar graph is symmetrical about the origin, then you can \r\n" );
document.write( "proceed either of two ways:\r\n" );
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document.write( "1.  Show that it is symmetrical about both the x and y axes.\r\n" );
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document.write( "OR\r\n" );
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document.write( "2.  Substitute -r for r, then simplify.  If it can then be simplified\r\n" );
document.write( "to the original equationb, then it is symmetrical about the origin.\r\n" );
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document.write( "Check for symmetry about the x-axis,\r\n" );
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document.write( "That's the same as the original equation, so it's symmetrical\r\n" );
document.write( "about the x-axis.\r\n" );
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document.write( "Check for symmetry about the y-axis,\r\n" );
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document.write( "That's not same as the original equation, so it's not symmetrical\r\n" );
document.write( "about the y-axis.\r\n" );
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document.write( "It's not symmetrical about both axes, so it's not symmetrical about the origin.\r\n" );
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document.write( "Edwin

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