Unit Circle Table
A complete reference table for the unit circle, showing exact and decimal values of sine, cosine, and tangent at all 17 standard angles from 0° to 360°. The unit circle is a circle of radius 1 centered at the origin, where each angle θ maps to the coordinates (cos θ, sin θ) on the circle.
Exact Values
Exact trigonometric values at the standard angles. Angles are given in both degrees and radians. Tangent is undefined where cosine equals zero.
| Degrees | Radians | sin θ | cos θ | tan θ | Quadrant |
|---|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 | — |
| 30° | π/6 | 1/2 | √3/2 | √3/3 | I |
| 45° | π/4 | √2/2 | √2/2 | 1 | I |
| 60° | π/3 | √3/2 | 1/2 | √3 | I |
| 90° | π/2 | 1 | 0 | undefined | — |
| 120° | 2π/3 | √3/2 | −1/2 | −√3 | II |
| 135° | 3π/4 | √2/2 | −√2/2 | −1 | II |
| 150° | 5π/6 | 1/2 | −√3/2 | −√3/3 | II |
| 180° | π | 0 | −1 | 0 | — |
| 210° | 7π/6 | −1/2 | −√3/2 | √3/3 | III |
| 225° | 5π/4 | −√2/2 | −√2/2 | 1 | III |
| 240° | 4π/3 | −√3/2 | −1/2 | √3 | III |
| 270° | 3π/2 | −1 | 0 | undefined | — |
| 300° | 5π/3 | −√3/2 | 1/2 | −√3 | IV |
| 315° | 7π/4 | −√2/2 | √2/2 | −1 | IV |
| 330° | 11π/6 | −1/2 | √3/2 | −√3/3 | IV |
| 360° | 2π | 0 | 1 | 0 | — |
Decimal Approximations
Decimal values rounded to 6 places. Useful when exact radical form is not required.
| Degrees | Radians | sin θ | cos θ | tan θ |
|---|---|---|---|---|
| 0° | 0.000000 | 0.000000 | 1.000000 | 0.000000 |
| 30° | 0.523599 | 0.500000 | 0.866025 | 0.577350 |
| 45° | 0.785398 | 0.707107 | 0.707107 | 1.000000 |
| 60° | 1.047198 | 0.866025 | 0.500000 | 1.732051 |
| 90° | 1.570796 | 1.000000 | 0.000000 | undefined |
| 120° | 2.094395 | 0.866025 | −0.500000 | −1.732051 |
| 135° | 2.356194 | 0.707107 | −0.707107 | −1.000000 |
| 150° | 2.617994 | 0.500000 | −0.866025 | −0.577350 |
| 180° | 3.141593 | 0.000000 | −1.000000 | 0.000000 |
| 210° | 3.665191 | −0.500000 | −0.866025 | 0.577350 |
| 225° | 3.926991 | −0.707107 | −0.707107 | 1.000000 |
| 240° | 4.188790 | −0.866025 | −0.500000 | 1.732051 |
| 270° | 4.712389 | −1.000000 | 0.000000 | undefined |
| 300° | 5.235988 | −0.866025 | 0.500000 | −1.732051 |
| 315° | 5.497787 | −0.707107 | 0.707107 | −1.000000 |
| 330° | 5.759587 | −0.500000 | 0.866025 | −0.577350 |
| 360° | 6.283185 | 0.000000 | 1.000000 | 0.000000 |
Signs by Quadrant
The sign of each function depends on which quadrant the angle falls in. The mnemonic ASTC ("All Students Take Calculus") gives the positive functions per quadrant:
| Quadrant | Degrees | sin | cos | tan |
|---|---|---|---|---|
| I | 0° – 90° | + | + | + |
| II | 90° – 180° | + | − | − |
| III | 180° – 270° | − | − | + |
| IV | 270° – 360° | − | + | − |
Key Identities
- Pythagorean: sin²θ + cos²θ = 1
- Degrees to radians: radians = degrees × π / 180
- Radians to degrees: degrees = radians × 180 / π
- Tangent definition: tan θ = sin θ / cos θ
- Coordinates on the unit circle: (x, y) = (cos θ, sin θ)