Archimedian Spirals:

Archimedean spiral represented on a polar graph The Archimedean spiral (also known as the arithmetic spiral) is a spiral named after the 3rd century BC Greek mathematician Archimedes. It is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant angular velocity.

source:
en.wikipedia.org

image:
mathamazement.com

Cardioids

Polar Graphs: Limaçons, Roses, Lemniscates, & Cardioids 1. Nicholas Portugal Precalculus Honors Period A7 POLAR GRAPHS 2.

source:
slideshare.net

image:
math.kennesaw.edu

Circles

Investigating Circles. Now we have seen the equation of a circle in the polar coordinate system. In the last two examples, the same equation was used to illustrate the properties of symmetry and demonstrate how to find the zeros, maximum values, and plotted points that produced the graphs.

source:
courses.lumenlearning.com

image:
meangreenmath.com