Unit circle

Math

Definition

The unit circle is a circle with radius 1 centered at the origin of the coordinate plane. It is the foundation for defining trigonometric functions, where any point on the circle can be written as (cos θ, sin θ) for angle θ measured from the positive x-axis.

Examples

  • At θ = 0°, the point on the unit circle is (1, 0), so cos(0°) = 1 and sin(0°) = 0
  • At θ = 90°, the point is (0, 1), so cos(90°) = 0 and sin(90°) = 1
  • The unit circle shows why sin²θ + cos²θ = 1 — it comes from the equation x² + y² = 1
Key Fact

Any point on the unit circle is (cos θ, sin θ), and x² + y² = 1

Related Terms

Unit circle values Reference angles Sine cosine tangent Trig values of any angle

Study This Concept

Practice unit circle with free review games in these units:

Algebra 2 Unit 9: Trigonometric Functions Pre-Calculus Unit 4: Trigonometric Functions