Maths · Trigonometry · Unit circle
How to read it. Each spoke is an angle from the positive x-axis. Radians sit inside the circle, degrees sit just outside the spoke, and the point (cos θ, sin θ) sits further out, in exact form.
Quadrant I triangles are the 30°, 45°, and 60° reference triangles. Sine of 30°, 45°, 60° runs 1/2, √2/2, √3/2. Cosine runs that pattern backwards. Other angles use the same reference values with a sign change.
A S T C — All Students Take Calculus. Quadrant I, all of sine, cosine, and tangent are positive. II, sine only. III, tangent only. IV, cosine only.
Toggles hide degrees, radians, or coordinates so you can quiz yourself. On a phone, drag the chart, or read the exact-value list under it (including tangent).
The sixteen standard angles, drawn the way a textbook poster draws them. A point at angle θ on the unit circle is (cos θ, sin θ). Hide a layer and try to recall it, then drill the same values in the unit circle trainer. The rest of the desk is on the maths hub.
Drill Unit circle trainer Exact values for 0°, 30°, 45° … 330°. Five modes, quadrant I first.A S T C — All, Sine, Tangent, Cosine. The pale wedges in quadrant I are the 30°, 45°, and 60° reference triangles.
Drag to move around the chart. The list below has every exact value.
| Degrees | Radians | (cos θ, sin θ) | tan θ |
|---|
A short SOHCAHTOA / identity check. On the unit circle the hypotenuse is 1, so sin θ is the y-coordinate and cos θ is the x-coordinate.
Pythagorean: sin²θ + cos²θ = 1. Every point on this circle is exactly 1 from the origin.
Tangent: tan θ = sin θ / cos θ when cos θ ≠ 0. That is why tan is undefined at 90° and 270°.
Cofunction: sin(90° − θ) = cos θ, and cos(90° − θ) = sin θ. That is the 30° / 60° swap.
Educational chart of the standard unit-circle values. Not a substitute for a course or an exam-board syllabus.