The unit circle

Hover over the points, to get information on the corresponing angles and trig values. Check the “More angles” box to get more information that even most mathematicians want to know.

import {make_unit_circle} from './components/make_unit_circle.js';
viewof more_angles = Inputs.toggle({
  label: "More angles:", value: false 
});
angle_data = FileAttachment(
  './components/angle_data.json').json();
make_unit_circle(angle_data, more_angles)

The image of the (extended) unit circle shown above is an interactive version of the one shown in many Calculus and Precalculus texts and much like the one shown in this Wikipedia image. On this one, though, you can hover your mouse over any of the points to reveal the corresponding angle \(\theta\) as well as the coordinates of the point, which are \((\cos(\theta),\sin(\theta))\). A geometric understanding of this circle makes it easier to remember formulae such as \[\sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}.\]

If you ever felt like your trig teacher didn’t make you memorize quite enough trig formulae, you can check the “More angles” box to see even more.