Frequently Asked Questions
Everything you need to know about the Interactive Unit Circle.
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.