Polar Systems and More
For questions 1-3, graph each pair of polar equations on the same polar grid. Find the polar coordinates of the
point(s) of intersection and label the point(s) on the graph. Then solve algebraically to verify the points. You may
get repeated points or extraneous points – identify these.
1) r  4cos  ; r 
1
cos 
2) r  2  2cos ; r  2sin 
3) r  3  3cos ; r  3  3sin 
Graph each equation by making a table of values. Honor system here, plot by hand, then compare with desmos.
4) r  csc  4 ; 0    
5) r   graph until you go off the grid.
Polar Systems and More
For questions 1-3, graph each pair of polar equations on the same polar grid. Find the polar coordinates of the
point(s) of intersection and label the point(s) on the graph. Then solve algebraically to verify the points. You may
get repeated points or extraneous points – identify these.
1) r  4cos  ; r 
1
cos 
2) r  2  2cos ; r  2sin 
3) r  3  3cos ; r  3  3sin 
Graph each equation by making a table of values. Honor system here, plot by hand, then compare with desmos.
4) r  csc  4 ; 0    
5) r   graph until you go off the grid.
Polar Systems and More
For questions 1-3, graph each pair of polar equations on the same polar grid. Find the polar coordinates of the
point(s) of intersection and label the point(s) on the graph. Then solve algebraically to verify the points. You may
get repeated points or extraneous points – identify these.
1) r  4cos  ; r 
1
cos 
2) r  2  2cos ; r  2sin 
3) r  3  3cos ; r  3  3sin 
Graph each equation by making a table of values. Honor system here, plot by hand, then compare with desmos.
4) r  csc  4 ; 0    
5) r   graph until you go off the grid.
Polar Systems and More
For questions 1-3, graph each pair of polar equations on the same polar grid. Find the polar coordinates of the
point(s) of intersection and label the point(s) on the graph. Then solve algebraically to verify the points. You may
get repeated points or extraneous points – identify these.
1) r  4cos  ; r 
1
cos 
2) r  2  2cos ; r  2sin 
3) r  3  3cos ; r  3  3sin 
Graph each equation by making a table of values. Honor system here, plot by hand, then compare with desmos.
4) r  csc  4 ; 0    
5) r   graph until you go off the grid.