# Graphing Calculator Drawing: Lissajous Curves

*Lissajous curves use sine functions to create interesting patterns in the plane.*

*This post is a chapter in the book Graphing Calculator Drawing Exercises.* *Suggested citation:* Skycak, J. (2019). Graphing Calculator Drawing: Lissajous Curves. *Graphing Calculator Drawing Exercises.* https://justinmath.com/graphing-calculator-drawing-lissajous-curves/

** Setup.** Navigate to https://www.desmos.com/calculator. Be sure to sign in so that you can save your graph.

** Demonstration - Lissajous Curves.** Lissajous curves take the form

for some values of $a$ and $b.$ Observe the graph as you type each of the following Lissajous plot inputs, with $0 \leq t \leq 100.$

** Exercise.** Attempt to reproduce the graphs below by setting $a=1$ and varying the $b$ parameter in the Lissajous curve equations. You may have to play with the parameter a bit to get a sense of what it controls.

** Exercise.** Attempt to reproduce the graphs below by setting $b=\frac{\pi}{2}$ and varying the $a$ parameter in the Lissajous curve equations. You may have to play with the parameter a bit to get a sense of what it controls.

** Challenge.** Attempt to reproduce the Lissajous graphs below by setting $b=1$ and varying $a.$

*This post is a chapter in the book Graphing Calculator Drawing Exercises.* *Suggested citation:* Skycak, J. (2019). Graphing Calculator Drawing: Lissajous Curves. *Graphing Calculator Drawing Exercises.* https://justinmath.com/graphing-calculator-drawing-lissajous-curves/