Unit Circle Values
Complete reference for sine, cosine, and tangent values at key angles (0°, 30°, 45°, 60°, 90° and beyond).
Essential trig reference table.
The Unit Circle
The unit circle is a circle with radius 1 centered at the origin.
For any angle θ, the point on the unit circle is (cos θ, sin θ).
Key Angle Values (First Quadrant)
| Degrees | Radians | sin θ | cos θ | tan θ |
|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 |
| 30° | π/6 | 1/2 | √3/2 | √3/3 |
| 45° | π/4 | √2/2 | √2/2 | 1 |
| 60° | π/3 | √3/2 | 1/2 | √3 |
| 90° | π/2 | 1 | 0 | undefined |
All Four Quadrants
| Degrees | sin θ | cos θ | tan θ |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 1/2 | √3/2 | √3/3 |
| 45° | √2/2 | √2/2 | 1 |
| 60° | √3/2 | 1/2 | √3 |
| 90° | 1 | 0 | undefined |
| 120° | √3/2 | -1/2 | -√3 |
| 135° | √2/2 | -√2/2 | -1 |
| 150° | 1/2 | -√3/2 | -√3/3 |
| 180° | 0 | -1 | 0 |
| 210° | -1/2 | -√3/2 | √3/3 |
| 225° | -√2/2 | -√2/2 | 1 |
| 240° | -√3/2 | -1/2 | √3 |
| 270° | -1 | 0 | undefined |
| 300° | -√3/2 | 1/2 | -√3 |
| 315° | -√2/2 | √2/2 | -1 |
| 330° | -1/2 | √3/2 | -√3/3 |
| 360° | 0 | 1 | 0 |
Sign Rules by Quadrant
Remember which functions are positive in each quadrant with the mnemonic: All Students Take Calculus
- Quadrant I (0° to 90°): All are positive
- Quadrant II (90° to 180°): Sin is positive
- Quadrant III (180° to 270°): Tan is positive
- Quadrant IV (270° to 360°): Cos is positive
Example 1
Find sin(150°)
150° is in Quadrant II. The reference angle is 180° - 150° = 30°.
sin is positive in Quadrant II.
sin(150°) = sin(30°) = 1/2
Example 2
Find cos(225°)
225° is in Quadrant III. The reference angle is 225° - 180° = 45°.
cos is negative in Quadrant III.
cos(225°) = -cos(45°) = -√2/2
When to Use It
Use the unit circle reference when:
- You need exact trig values without a calculator
- Solving trig equations and finding all solutions
- Determining the sign of a trig function in a given quadrant
- Converting between degrees and radians