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.

Unit Circle Chart 12
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

Unit circle chart 4

Unit Circle Chart 8

Unit circle chart 8

Unit Circle Chart 12

Unit circle chart 12

Generalizing the Problem

At this point, you can continue dividing the unit circle into more subdivisions like , , or and find the coordinates corresponding to each angle. This by itself is useful because if your method for calcuating 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.

Unit Circle Chart Point

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…

Unit Circle Chart Trigonometry