Unit Circle Chart

The unit circle chart shows the positions of the points on the unit circle that are formed by dividing the circle into equal parts. The angles on the charts shown on this page are measured in radians.

Note: This site uses the circle constant (tau) instead of (pi) when measuring angles in radians. The substitution can be used to translate between the two constants. If you want to see the unit circle chart annotated with instead, see this page.

Unit Circle Chart 4

This chart shows the angles and points formed by dividing the unit circle into four equal parts.

Unit Circle Chart 8

This chart shows the angles and points formed by dividing the unit circle into eight equal parts.

Unit Circle Chart 12

This chart shows the angles and points formed by dividing the unit circle into twelve equal parts.

Generalizing the Problem

At this point, you can continue dividing the unit circle into more subdivisions like 24, 100, or 360 and find the coordinates corresponding to each angle. This by itself is useful because if your method for calculating coordinates is accurate enough these values can be used in real-world applications.

These calculations are also a primer for the generalized form of this problem. Given an angle (theta) on the unit circle, what are the coordinates of the point corresponding to the angle? This is a genuinely hard problem and finding a general solution is difficult.

This is a genuinely hard problem and finding a general solution is difficult. As a result, in modern-day math the two functions sine and cosine exist to answer exactly that problem. Given an angle as input, sine returns the vertical component and cosine returns the horizontal component of the point on the unit circle corresponding to the angle. Read more…