⭕ Unit Circle Reference
Enter any angle to get sine, cosine and tangent, plus the (x, y) point on the unit circle. The table below shows the common "nice" angles for quick reference.
The point on the circle is the answer
On a circle of radius 1 the coordinates of a point are its cosine and sine, and tangent is the ratio between them:
(x, y) = (cos θ, sin θ) tan θ = sin θ / cos θ = y / x
radians = degrees × π / 180At the default 45°, x and y are equal, so sin and cos both read 0.70711 and tan is exactly 1. The angle itself is echoed back in both units - 45° is 0.785398 radians - and the radian input accepts values like 1.0472 for 60°.
Exact values behind the decimals
The reference table gives decimals; these are the surds they stand for.
| 0.5 | 0.70711 | 0.86603 | 0.57735 | 1.73205 |
|---|---|---|---|---|
| 1/2 | √2 / 2 | √3 / 2 | √3 / 3 | √3 |
- Signs follow the quadrant. All three are positive from 0 to 90°; then only sine, then only tangent, then only cosine.
- Watch the order of the point. It is written (cos, sin), so cosine is the horizontal value even though sine is usually named first.
Frequently asked questions
What is sin 45 degrees?
0.70711, which is exactly the square root of 2 divided by 2. Cosine is the same at 45 degrees, which is why tangent comes out at 1.
Why is tan 90 degrees undefined?
Tangent is sine over cosine, and cosine is 0 at 90 degrees. The point sits at the top of the circle, directly above the centre, so there is no slope to report.
How do I convert degrees to radians?
Multiply by pi and divide by 180. That makes 45 degrees 0.785398 radians and 180 degrees exactly pi.