Thomas Calculus 13th [Solutions]

Section 11.4 Graphing Polar Coordinate Equations 825
11.4 GRAPHING POLAR COORDINATE EQUATIONS
1. 1 cos( ) 1 cos r symmetric about the x-axis;
1 cos( ) r and 1 cos( ) 1 cos r not symmetric
about the y -axis; therefore not symmetric about the origin
2. 2 2cos( ) 2 2cos r symmetric about the x-axis;
2 2cos( ) r and 2 2cos( ) 2 2cos r
not symmetric about the y -axis; therefore not symmetric
about the origin
3. 1 sin( ) 1 sin r and 1 sin ( ) 1 sin r
not symmetric about the x -axis; 1 sin( ) 1 sin r
symmetric about the y -axis; therefore not symmetric
about the origin
4. 1 sin( ) 1 sin r and 1 sin( ) 1 sin r
not symmetric about the x -axis; 1 sin( ) 1 sin r
symmetric about the y -axis; therefore not symmetric about the origin
5. 2 sin( ) 2 sin r and 2 sin( ) 2 sin r not
symmetric about the x -axis; 2 sin( ) 2 sin r symmetric
about the y -axis; therefore not symmetric about the origin
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