Lines

Horizontal lines

$$\graph [polar]{a=1,r=a \csc (\theta )}$$

Vertical lines

$$\graph [polar]{a=1,r=a \sec (\theta )}$$

Not through the origin

$$\graph [polar]{b=1,m=1,r=\frac {b}{\sin (\theta )-m \cos (\theta )}}$$

Circles

Centered on the x-axis

$$\graph [polar]{a=1, r=a \cos (\theta )}$$

Centered on the y-axis

$$\graph [polar]{a=1,r=a \sin (\theta )}$$

Centered at the origin

$$\graph [polar]{a=1,r=a}$$

Archimedean spiral

$$\graph [polar]{r=\theta }$$

Limaçons

With inner loop

$$\graph [xmin=-5,xmax=5,ymin=-2,ymax=2,polar]{a=1,b=2,r=a+b \cos (\theta )}$$ $$\graph [xmin=-5,xmax=5,ymin=-.5,ymax=3.5,polar]{a=1,b=2,r=a+b \sin (\theta )}$$

Cardioid

$$\graph [xmin=-5,xmax=5,ymin=-2,ymax=2,polar]{a=1,b=a,r=a+b \cos (\theta )}$$ $$\graph [xmin=-5,xmax=5,ymin=-1,ymax=2.5,polar]{a=1,b=a,r=a+b \sin (\theta )}$$

Dimpled

$$\graph [polar]{a=3,b=2,r=a+b \cos (\theta )}$$ $$\graph [xmin=-10,xmax=10,ymin=-2,ymax=6,polar]{a=3,b=2,r=a+b \sin (\theta )}$$

Convex

$$\graph [xmin=-20,xmax=20,ymin=-7.5,ymax=7.5,polar]{a=5,b=2,r=a+b \cos (\theta )}$$ $$\graph [xmin=-20,xmax=20,ymin=-5.5,ymax=10,polar]{a=5,b=2,r=a+b \sin (\theta )}$$

Rose curves

$$\graph [xmin=-5,xmax=5,ymin=-2,ymax=2,polar]{r=\cos (2\theta )}$$

$$\graph [xmin=-5,xmax=5,ymin=-2,ymax=2,polar]{r=\sin (2\theta )}$$

$$\graph [xmin=-5,xmax=5,ymin=-2,ymax=2,polar]{r=\cos (3\theta )}$$

$$\graph [xmin=-5,xmax=5,ymin=-2,ymax=2,polar]{r=\sin (3\theta )}$$