11.5 Graphs of Polar Equations:

I. Circles: 

Example 1.

        Equation(s): 

        Modes: Pol, Radians

        Range: 

        X-Y Coordinates:

        Points on graph: 

        
 

Example 2.

        Equation(s): 

        Modes: Pol, Radians

        Range: 

        X-Y Coordinates:
 

 
II. Archimedes Spiral: 

Example 3.

        Equation(s): 

        Modes: Pol, Radians

        Range: 

        X-Y Coordinates:

        Points on graph:

                

                

                
 
                
 

Examples 4 - 6

Plot the following in the same window above: 


 


 


 

 
III. Limacons: 

Example 7.

        Equation(s): 

        Modes: Pol, Radians

        Range: 

        X-Y Coordinates:

        Points on graph:

                

                

                

                
 

Plot in same window as above:

Example 8-11:

    
 

 
 

    
 

    
 

 

IV. Rose Curve: 

Example 12.

        Equation(s): 

        Modes: Pol, Radians

        Range: 

        X-Y Coordinates:

        Point on graph:
 

Example 13.

        Equation(s): 

        Modes: Pol, Radians

        Range: 

        X-Y Coordinates:

        Points on graph, r =
 

 

Example 14
 

Example 15.

        Equation(s): 

        Modes: Pol, Radians

        Range: 

        X-Y Coordinates:

        Point on graph::
 

 
V. Lemsicate: Examples 16 & 17 r2=a2sin 2 x,    r2=a2cos 2 x