Unit circle values table
| Degrees | Radians | sin θ | cos θ | tan θ |
|---|
What is the unit circle?
The unit circle is a circle with radius 1 centered at the origin. Measure an angle θ counterclockwise from the positive x-axis. The point where its terminal side crosses the circle is (cos θ, sin θ). That single fact defines sine and cosine for every angle, not just the acute angles of a right triangle.
Why the coordinates are cos and sin
Drop a perpendicular from the point to the x-axis. You get a right triangle with hypotenuse 1, so the adjacent side is cos θ and the opposite side is sin θ. In the diagram the blue segment is cos θ and the red segment is sin θ.
Where tangent appears
tan θ = sin θ / cos θ. Geometrically it is the length of the green segment on the line x = 1, cut off by extending the terminal side. It is undefined at 90° and 270°, where the terminal side is parallel to that line.
How to memorize the unit circle
- Learn the first quadrant. For 30°, 45° and 60° the sines are √1/2, √2/2 and √3/2, and the cosines run in the opposite order.
- Use the reference angle. Every other angle reuses one of those values. 150° has reference angle 30°, so its sine and cosine have magnitudes 1/2 and √3/2.
- Fix the signs by quadrant. "All Students Take Calculus": all positive in QI, only sine in QII, only tangent in QIII, only cosine in QIV.
Degrees and radians
A full turn is 360° or 2π radians, so multiply degrees by π/180 to convert to radians. You can type angles in either form above, for example 135, 3pi/4 or 2.36 rad. Negative angles and angles larger than 360° work too and are shown with their coterminal angle.
FAQ
Can I print the unit circle chart?
Yes. Tick Full chart and press Download PNG to save a high-resolution chart with all 16 standard angles, their radian measures and coordinates.
Why do some angles show exact values and others only decimals?
Exact forms built from square roots exist for every multiple of 15°. Other angles have no simple closed form, so the tool shows the decimal value.