Unit Circle Calculator
Enter any angle in degrees or radians to see where it lands on the unit circle. The $x$-coordinate equals $\cos\theta$ and the $y$-coordinate equals $\sin\theta$.
What Is the Unit Circle?
The unit circle is a circle with radius 1 centered at the origin. For any angle $\theta$ measured counter-clockwise from the positive $x$-axis, the point where the terminal side intersects the circle has coordinates $(\cos\theta,\, \sin\theta)$. This extends trig to all angles, not just the acute angles of a right triangle.
$$x = \cos\theta, \quad y = \sin\theta, \quad \tan\theta = \frac{y}{x} = \frac{\sin\theta}{\cos\theta}$$The Four Quadrants
| Quadrant | Angle range | cos θ | sin θ | tan θ |
|---|---|---|---|---|
| I | 0° – 90° | + | + | + |
| II | 90° – 180° | − | + | − |
| III | 180° – 270° | − | − | + |
| IV | 270° – 360° | + | − | − |
Use the Sin Cos Tan calculator to compute all six trig functions at once, or the degrees to radians converter if you need to convert your angle first.
Common Angles on the Unit Circle
| Degrees | Radians | cos θ | sin θ | tan θ |
|---|---|---|---|---|
| 0° | 0 | 1 | 0 | 0 |
| 30° | π/6 | √3/2 | 1/2 | 1/√3 |
| 45° | π/4 | √2/2 | √2/2 | 1 |
| 60° | π/3 | 1/2 | √3/2 | √3 |
| 90° | π/2 | 0 | 1 | undef. |
| 180° | π | −1 | 0 | 0 |
| 270° | 3π/2 | 0 | −1 | undef. |
| 360° | 2π | 1 | 0 | 0 |
