⭕Interactive Unit Circle
Click any of the 16 standard angles, or drag the point freely, to see exact sine, cosine, and tangent values with a reference triangle.
| Exact | Decimal | |
|---|---|---|
| sin θ | 0 | 0.000 |
| cos θ | 1 | 1.000 |
| tan θ | 0 | 0.000 |
Free Interactive Unit Circle
The unit circle is the fastest way to memorize exact trig values — our interactive version lets you click any standard angle to instantly see its exact sine, cosine, and tangent, both as fractions with radicals and as decimals.
Click through all 16 standard angles (multiples of 30° and 45°) around the full circle, or drag the point freely to explore any angle in between, watching the coordinates and trig values update live. A reference right-triangle overlay shows exactly how the coordinates connect to sine and cosine, and quadrant sign indicators make the ASTC rule (All Students Take Calculus) visual instead of memorized.
Switch instantly between degrees and radians, with radians shown as clean π fractions. Whether you're studying for a trig test or just need a quick lookup, it's free, requires no sign-up, and works entirely in your browser. See the About page or the FAQ for more.
About the Interactive Unit Circle
Features
16 standard angles
Every multiple of 30° and 45° 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 ⇄ radians
Toggle instantly between the two, with radians shown as clean π fractions.
Quadrant sign rules
The ASTC rule for which of sin, cos, and tan are positive in each quadrant, shown live.
Frequently Asked Questions
What is the unit circle?
A circle of radius 1 centered at the origin, used to define sine, cosine, and tangent for any angle.
How do I use this tool?
Click any of the 16 standard angle points, or drag the point freely, to see the exact trig values for that angle.
Are the values exact or decimals?
Both: exact fractions with radicals (e.g. √3/2) are shown alongside decimal equivalents.
Can I switch between degrees and radians?
Yes, a toggle switches every displayed value, with radians shown as π fractions.
What is the reference triangle?
It shows the right triangle formed by the angle, connecting the (x, y) coordinates to sine and cosine directly.
What are the ASTC quadrant signs?
A memory rule for which of sine, cosine, tangent are positive in each quadrant — shown visually here.
Is tangent always defined?
No — it's undefined at 90° and 270°, where cosine is zero; the tool states this clearly.
Can I use this on a touchscreen?
Yes, tap or drag works the same as clicking on desktop.
Is it free?
Completely free, no sign-up or limits.
Does it work on mobile?
Yes, fully responsive.