Graphs of polar equations

Graphing polar equations is much different than graphing regular (x,y) equations. 

Let's say we were given the equation: r=4sin theta

Now remember that for sin, the value of theta is between 0<theta<2pi

By substituting various values of pi into the equation, we can also figure out the value of r for each calculated value of theta. Remember to plot the points according to polar coordinate system. So if theta is pi/6, r would be 2. That particular point is (2, pi/6)

Symmetry

1. Line theta = pi/2: replace (r, theta) with (r, pi - theta) 

2. The polar axis:    Replace (r,theta ) with (r, -theta)

3. The pole:            Replace (r, theta) with (r, pi + theta)

Let's try to see if the equation: r=3+2cos theta has any symmetry

2. R = 3 + 2cos(-theta)

    R = 3 + 2cos theta. 

So it is symmetrical to the polar axis. 

To find the maximums of |r| we have to plug in different values of theta according to the range and see which value of r is the highest.

Shapes: