Unit Circle Reference Tool – Interactive Unit Circle Chart
Explore the complete unit circle with our free interactive unit circle reference tool. View all key angles in degrees and radians with their exact trig values and coordinates.
| Angle (°) | Angle (rad) | cos(θ) | sin(θ) | tan(θ) | Coordinates |
|---|---|---|---|---|---|
| 0° | 0 | 1 | 0 | 0 | (1, 0) |
| 30° | π/6 | √3/2 | 1/2 | √3/3 | (0.866, 0.5) |
| 45° | π/4 | √2/2 | √2/2 | 1 | (0.707, 0.707) |
| 60° | π/3 | 1/2 | √3/2 | √3 | (0.5, 0.866) |
| 90° | π/2 | 0 | 1 | undefined | (0, 1) |
| 120° | 2π/3 | -1/2 | √3/2 | -√3 | (-0.5, 0.866) |
| 135° | 3π/4 | -√2/2 | √2/2 | -1 | (-0.707, 0.707) |
| 150° | 5π/6 | -√3/2 | 1/2 | -√3/3 | (-0.866, 0.5) |
| 180° | π | -1 | 0 | 0 | (-1, 0) |
| 210° | 7π/6 | -√3/2 | -1/2 | √3/3 | (-0.866, -0.5) |
| 225° | 5π/4 | -√2/2 | -√2/2 | 1 | (-0.707, -0.707) |
| 240° | 4π/3 | -1/2 | -√3/2 | √3 | (-0.5, -0.866) |
| 270° | 3π/2 | 0 | -1 | undefined | (0, -1) |
| 300° | 5π/3 | 1/2 | -√3/2 | -√3 | (0.5, -0.866) |
| 315° | 7π/4 | √2/2 | -√2/2 | -1 | (0.707, -0.707) |
| 330° | 11π/6 | √3/2 | -1/2 | -√3/3 | (0.866, -0.5) |
| 360° | 2π | 1 | 0 | 0 | (1, 0) |
The unit circle is a circle with radius 1 centered at the origin. Every point on the circle has coordinates (cos θ, sin θ) where θ is the angle from the positive x-axis.
The x-coordinate equals cosine of the angle. The y-coordinate equals sine of the angle. Tangent is y/x or sin/cos. This geometric representation makes trig functions intuitive.
Notice the patterns. In quadrant I, all values are positive. In quadrant II, only sine is positive. In quadrant III, only tangent is positive. In quadrant IV, only cosine is positive. Remember "All Students Take Calculus" for the positive functions.
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