Unit Circle Table

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.

Note: This website uses the constant (tau) instead of (pi) as the default circle constant. The substitution can be used to translate between the two constants.

Common Angles

Fractions of 8

This table shows the angles and their corresponding points formed from dividing the unit circle into equal parts.

Fractions of 12

This table shows the angles and their corresponding points formed from dividing the unit circle into equal parts.

Explanation

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.

Lookup Table

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.

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