The unit circle table lists the coordinates of the points on the unit circle that correspond to common angles. The unit circle demonstrates the output of the trigonometric functions sine and cosine as discussed on this page. The table below shows angles measured using both degrees and radians and can be visualized by this chart.
| Degrees | Radians | ||
|---|---|---|---|
This table shows the angles and their corresponding points formed from dividing the unit circle into equal parts.
| Degrees | Radians | ||
|---|---|---|---|
This table shows the angles and their corresponding points formed from dividing the unit circle into equal parts.
| Degrees | Radians | ||
|---|---|---|---|
A point on the unit circle that corresponds to the angle (theta) is given by the sine and cosine of the angle as discussed on this page. This concept is visualized in the illustration and equations below.
Historically, the trigonometric ratios represented by the trigonometric functions cosine and sine would have been looked up in a table. For, example the lookup table below shows the trigonometric ratios for angles in the first quadrant of the circle.
| Angle | Radians | Sine | Cosine |
|---|---|---|---|
0° |
0.000 TAU |
0.000 |
1.000 |
5° |
0.014 TAU |
0.087 |
0.996 |
10° |
0.028 TAU |
0.174 |
0.985 |
15° |
0.042 TAU |
0.259 |
0.966 |
20° |
0.056 TAU |
0.342 |
0.940 |
25° |
0.069 TAU |
0.423 |
0.906 |
30° |
0.083 TAU |
0.500 |
0.866 |
35° |
0.097 TAU |
0.574 |
0.819 |
40° |
0.111 TAU |
0.643 |
0.766 |
45° |
0.125 TAU |
0.707 |
0.707 |
50° |
0.139 TAU |
0.766 |
0.643 |
55° |
0.153 TAU |
0.819 |
0.574 |
60° |
0.167 TAU |
0.866 |
0.500 |
65° |
0.181 TAU |
0.906 |
0.423 |
70° |
0.194 TAU |
0.940 |
0.342 |
75° |
0.208 TAU |
0.966 |
0.259 |
80° |
0.222 TAU |
0.985 |
0.174 |
85° |
0.236 TAU |
0.996 |
0.087 |
90° |
0.250 TAU |
1.000 |
0.000 |