Polar Graphs

Recently in PreCalc we have been learning about polar graphs. We began a project on Desmos.com where we were to use specific equations to observe their effects on the shape.

first I simply began with the equation r=asin(b*theta) which resulted in the following;

Moving the "a" slider increased the size of the "rose" and the "b" slider resulted in that number of loops per two quadrants or half graph.

After learning other basic equations such as r=asin(b*theta) and r=acos(b*theta) and the Spiral of Archimedes (r=theta), and Limacon graphs: r=a+bsin(theta) and r=a+bcos(theta), we were to create an intricate flower pattern. Mine turned out as the following;

I chose to play around with the equations to see what other forms the graph could produce, I used many equations which are depicted below;

When moving the "a" and "b" sliders at the same time my graph morphed into cool shapes and the psychedelic pattern came to life. I really enjoyed this project and using desmos it made learning the equations simple and entertaining, and I really like my final result.