Graphing Calculator Drawing: Composition Waves and Implicit Trig Patterns

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

Demonstration - Composition Waves. Observe the graph as you type each of the following inputs.

$\begin{align*} &y=\sin(x) \\[10pt] &y=\sin(x^2) \\[10pt] &y=\sin\left( \frac{1}{x} \right) \\[10pt] &y=\sin\left( \tan(x) \right) \\[10pt] &y = \tan\left( \sin(x) \right) \end{align*}$


Demonstration - Implicit Trig Patterns. Observe the graph as you type each of the following inputs.

$\begin{align*} &\sin(y)=\cos(x) \\[10pt] &\sin(y)=\tan(x) \\[10pt] &\sin\left(y\right)=\sin\left(x+y\right) \\[10pt] &\sin\left(y\right)\tan\left(x\right)=\cos\left(x\right)\tan\left(y\right) \\[10pt] &\sin\left(y\right)\cos\left(x\right)=0.1 \\[10pt] &\sin\left(xy\right)=\sin\left(x+y\right) \end{align*}$


Challenge. Create some interesting wallpapers using implicit trig patterns!

This post is part of a series.