Interactive Unit Circle
Explore the unit circle interactively to understand trigonometry.
The heart of trigonometry
The unit circle — a circle of radius one — is the key to understanding trigonometry, tying angles to the sine and cosine functions in a single picture. This lets you explore it interactively, moving around the circle to see how the trig values change.
Move around the circle to see the angles and values.
Why the unit circle unlocks trig
Trigonometry defined only through right triangles hits a wall — it cannot handle angles beyond 90 degrees, or negative angles. The unit circle solves this elegantly: for any angle, a point moves around the circle, and its horizontal position is the cosine and its vertical position is the sine. Suddenly every angle works, the values naturally range between minus one and one, and the repeating, wave-like nature of sine and cosine becomes obvious as the point goes round and round. It makes sense of why these functions are periodic, where they are positive or negative, and the exact values at the special angles. Interacting with it, watching the values change as you move around, is the single most effective way to build genuine intuition for trigonometry rather than memorising a table.
Common questions
Why is the unit circle so important in trigonometry?
It extends sine and cosine to any angle — a point's horizontal position is the cosine and its vertical position the sine — beyond what right triangles allow.
What does it make clear?
Why sine and cosine are periodic and wave-like, where they are positive or negative, and their values at special angles — all visible as the point moves round.
Is anything uploaded?
No. It runs entirely in your browser.