Unit Circle Calculator
Sin, cos, tan from degrees on radius 1.
What it does
The unit circle compresses all of trigonometry into radius 1: every angle lands on a point whose x reads cosine and y reads sine. Tangent follows as the slope between them.
The tool above takes degrees. It returns sine, cosine, and tangent with radians in the note.
The default 45 gives 0.7071 and 0.7071 with tangent 1. The 30 case gives 0.5, 0.866, and 0.5774, while 180 gives 0, minus 1, and 0.
Trigonometry texts define the functions exactly this way around the circle, with LibreTexts and OpenStax walking the same coordinates. Special angles fall out as root fractions, not decimals to memorize.
Undefined tangent at 90 and 270 is honest math, not missing data: cosine hits zero there. Quadrant signs follow All Students Take Calculus from the first quadrant on.
How to use
- Type degrees 0 to 360.
- Read sine first.
- Read cosine beside it.
- Read tangent last.
- Watch undefined at 90, 270.
- Convert with pi over 180.
Formula
- deg
- Angle in degrees, 0 to 360.
- rad
- Angle in radians.
- sin/cos/tan
- y, x, and y/x on radius 1.
LibreTexts trigonometry and OpenStax precalculus build sine and cosine as unit circle coordinates with tangent as their ratio. The 45, 30, and 180 checks match the exact root values. Undefined tangent at odd quarter turns reflects division by zero, reported plainly.
Worked example
Example: 45 degrees
Default: 45 degrees.
- Angle: 45 degrees.
- Radians: 45 x pi / 180 = 0.7854.
- Sine: sin(45) = 0.7071.
- Cosine: cos(45) = 0.7071.
- Tangent: 0.7071 / 0.7071 = 1.
- Tool shows 0.7071, 0.7071, 1.
Reference table
| Degrees | Sin | Cos | Tan |
|---|---|---|---|
| 0 | 0 | 1 | 0 |
| 30 | 0.5 | 0.866 | 0.5774 |
| 45 | 0.7071 | 0.7071 | 1 |
| 60 | 0.866 | 0.5 | 1.7321 |
| 90 | 1 | 0 | Undefined |
Limits
- Degrees 0 to 360.
- Radius 1 only.
- Principal values, no identities.
- Rounding at 4 decimals.
Common mistakes
- Reading tan at 90 as zero.
- Mixing degrees with radians.
- Forgetting quadrant signs.
- Expecting exact radicals.
- Scaling radius away from 1.
Try it yourself
Quick checks. Answers sit tucked under each question.
30 degrees?
0.5, 0.866, 0.5774.
180 degrees?
0, minus 1, 0.
400 degrees?
Past full turn: enter 0 to 360 degrees.
Questions
Reading the circle?
Coordinates of the angle on radius 1: x is cosine, y is sine, slope y/x is tangent.
Radians?
Multiply by pi over 180. 45 gives 0.7854 rad.
30 degrees?
0.5, 0.866, 0.5774: the classic 30 triangle.
180 degrees?
Sine hits 0 with cosine minus 1; tangent lands 0 too.
Tangent undefined?
At 90 and 270 cosine hits 0, so tangent is undefined. The tool says so.
Signs by quadrant?
ASTC signs per quadrant: all, sine, tangent, cosine going I to IV.