Unit Circle Chart (Labeled)
Every standard angle on the unit circle, labelled with its exact (cosine, sine) coordinates.
How to read the unit circle
- Pick an angle, measured counterclockwise from the positive x-axis.
- Find where that angle meets the circle — its coordinates are (cos θ, sin θ).
- The x-coordinate is always cosine, the y-coordinate is always sine, for every angle on the circle.
Worked example: 60°
At 60°, the point on the unit circle is (1/2, √3/2). That means cos 60° = 1/2 and sin 60° = √3/2 — no calculator needed, since these are exact values from the 30-60-90 triangle.
Watch the point trace the circle and the matching sine wave build up live in the Unit Circle tool.
Frequently asked questions
What is the unit circle?
A circle of radius 1 centred at the origin. For any angle measured from the positive x-axis, the point where it meets the circle has coordinates (cos θ, sin θ).
Why is the radius exactly 1?
It makes the x-coordinate equal to cosine and the y-coordinate equal to sine directly, with no scaling — that is the whole point of using a unit (length 1) circle.
How do you remember the unit circle values?
Learn the first quadrant (0°, 30°, 45°, 60°, 90°) by the pattern √0/2, √1/2, √2/2, √3/2, √4/2 for sine (simplified: 0, 1/2, √2/2, √3/2, 1), then mirror the signs into the other three quadrants.
Which quadrants have negative sine or cosine?
Cosine (x) is negative in quadrants II and III (90°–270°); sine (y) is negative in quadrants III and IV (180°–360°).
