Trigonometry · Quick Reference

Unit Circle Cheat Sheet

Trigonometry · Lesson 2/8

In one line: the unit circle is a circle of radius 1 centered at the origin — it extends sine and cosine beyond right triangles to work for any angle at all.

Key Ideas

1Definition. A circle with radius exactly 1, centered at the origin (0,0) of the coordinate plane.

2Coordinates on the Unit Circle. For any angle theta measured from the positive x-axis, the point on the unit circle is (cos(theta), sin(theta)).

3Radians vs. Degrees. Radians measure angles using the circle's radius as a unit; 360° = 2*pi radians, so 180° = pi radians.

4Key Angle Values. 0°=0 radians, 90°=pi/2 radians, 180°=pi radians, 270°=3pi/2 radians, 360°=2*pi radians.

5Signs in Each Quadrant. Quadrant I: both sin and cos positive. Quadrant II: sin positive, cos negative. Quadrant III: both negative. Quadrant IV: sin negative, cos positive.

Worked Examples

Convert 90° to radians.

pi/2 radians

Find the coordinates on the unit circle at angle 0°.

(1, 0)

In which quadrant is sin positive and cos negative?

Quadrant II

Formulas

360° = 2*pi radians

Point on unit circle at angle theta: (cos(theta), sin(theta))

Practice Yourself

Convert 180° to radians.

pi radians

Convert 360° to radians.

2*pi radians

Find the coordinates on the unit circle at 90°.

(0, 1)