About the Interactive Unit Circle

A clickable, draggable diagram for learning exact trig values at every standard angle.

What it is

The unit circle is a circle of radius 1 centered at the origin. For any angle ฮธ measured from the positive x-axis, the point where the angle's ray crosses the circle has coordinates (cos ฮธ, sin ฮธ) โ€” this is the definition trigonometry builds on. This tool lets you explore that relationship interactively instead of memorizing a static chart.

Features

16 standard angles

Every multiple of 30ยฐ and 45ยฐ around the full circle, each clickable and keyboard-navigable.

Exact values

Sine and cosine shown as exact fractions with radicals, alongside their decimal equivalents.

Draggable free-angle mode

Drag the point anywhere on the circle to see live decimal values, with snapping near standard angles.

Reference triangle

A right triangle overlay connects the (x, y) coordinates to sine and cosine visually.

Degrees โ‡„ radians

Toggle instantly between the two, with radians shown as clean ฯ€ fractions.

Quadrant sign rules

The ASTC rule for which of sin, cos, and tan are positive in each quadrant, shown live.

Ready to use it?

Free, no sign-up required.

Open the Interactive Unit Circle