Extend trigonometry beyond right triangles
The unit circle is a circle with radius 1 centered at the origin. It's fundamental to understanding trigonometry.
For any angle , if the terminal side intersects the unit circle at point :
| Angle (radians) | Angle (degrees) | (cos, sin) |
|---|---|---|
| 0 | 0° | (1, 0) |
| 30° | ||
| 45° | ||
| 60° | ||
| 90° | (0, 1) | |
| 180° | (-1, 0) | |
| 270° | (0, -1) | |
| 360° | (1, 0) |
| Quadrant | sin | cos | tan |
|---|---|---|---|
| I | + | + | + |
| II | + | - | - |
| III | - | - | + |
| IV | - | + | - |
Mnemonic: "All Students Take Calculus"
The reference angle is the acute angle formed with the x-axis.
Use reference angles to find trig values in any quadrant: