Circle and Waves

The unit circle is a circle with a radius of 1.

This picture is a cloud of paint. You can , , , , , , and .

Shelf: Math
Kind: Built from a recipe
Your own: Your own path
Sound: Yes
Hands-on: Yes
Licenses: Own work (made in the page)

How to play

Tap to send the point round. Hands-on: drag the point round; the waves follow.

Its controls

Control	Kind	Range	Start
Go round	Tap
Turn	Button
View	List	2 choices	2D diagram
Path	List	6 choices	Circle
Turns	Setting

About it

The unit circle is a circle with a radius of 1. As a point goes around it, turning through an angle called θ, its height is the sine of θ and its left-right place is the cosine. Traced out over time, they make two waves, the same shapes as sound and light waves.

Tap it and the point goes once around while its height draws the sine wave and its left-right place draws the cosine wave. For the circle, Euler's formula, e^(iθ) = cos θ + i sin θ, lights up piece by piece. In the Splash tab, try a 3D helix, another path, up to three turns, or type your own: x = …, y = … with t, or r = … with θ.

Details

Splats: Opens at 200,000 at Mid Detail, 60,000 at Low, and up to 590,000 at Max
Your own files: .txt

Sources and credits

Made in Splashery. Its code is MIT.

Share it

This link opens it in the Playground. To put it on your own page, add the element and one script tag. Every option.

https://splashery.app/play/?toy=unit-circle

<script type="module" src="https://splashery.app/play/src/element.js"></script>
<splashery-toy toy="unit-circle"></splashery-toy>