Thomas Calculus 13th [Solutions]

826 Chapter 11 Parametric Equations and Polar Coordinates
6. 1 2sin( ) 1 2sin r and 1 2sin( ) 1 2sin r not
symmetric about the x -axis; 1 2sin( ) 1 2sin r
symmetric about the
y -axis; therefore not symmetric about the origin
7.
sin sin r symmetric about the y-axis;
2 2
sin 2 sin , so the graph is symmetric about the x -axis, and
2 2
hence the origin.
8.
cos cos r symmetric about the x-axis;
2 2
cos 2 cos , so the graph is symmetric about the y -axis, and
2 2
hence the origin.
9.
2
cos( ) cos r ( r , ) and ( r , ) are on the graph when
( r , ) is on the graph symmetric about the x -axis and y-axis;
therefore symmetric about the origin
10.
2
sin( ) sin r ( r , ) and ( r , ) are on the graph
when ( r , ) is on the graph symmetric about the y -axis and the
x -axis; therefore symmetric about the origin
11.
2
sin( ) sin r ( r , ) and ( r , ) are on the graph
when ( r , ) is on the graph symmetric about the y -axis and the
x -axis; therefore symmetric about the origin
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