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.