Steven Philley
Maths Trig Linear algebra Calculus Site contents

Maths · Trigonometry · Unit circle

Unit circle

On the unit circle (radius 1), a point at angle θ from the positive x-axis is (cos θ, sin θ). Drag the handle — or use presets — and watch sine, cosine, and tangent update. Pair with the maths hub.

Interactive circle

Drag on the canvas, or use arrow keys after focusing the canvas (← → nudge 1°, Shift for 15°).

Readout

Common angles

Remember

SOH · CAH · TOA — opposite/hypotenuse, adjacent/hypotenuse, opposite/adjacent in a right triangle. On the unit circle, hypotenuse is 1, so sin = y and cos = x.

Check yourself

A short SOHCAHTOA / identity check. Answers use exact common values where possible.

Useful identities

Pythagorean: sin²θ + cos²θ = 1 (always true on the unit circle — watch the live check in the readout).

Tangent: tan θ = sin θ / cos θ when cos θ ≠ 0.

Cofunction: sin(90° − θ) = cos θ, and cos(90° − θ) = sin θ (in degrees).

Nearby

Maths hub Linear algebra Calculus Site contents

Educational interactive — original explanations of standard trig facts. Not a substitute for a course or exam board syllabus.