Library/Algebra/Trigonometry/Trigonometric circle

Trigonometric circle

Overview
Important

The trigonometric circle (also called the unit circle) is the circle in the coordinate plane with center at the origin and radius 1. For any real angle θ\theta, the point on the circle at that angle from the positive x-axis has coordinates (cos⁡θ,sin⁡θ)(\cos \theta, \sin \theta). This allows us to define sine and cosine for all real angles, not just those in right triangles.

Important properties

  • The equation of the trigonometric circle is x2+y2=1x^2 + y^2 = 1.

  • For any angle θ\theta, the coordinates (cos⁡θ,sin⁡θ)(\cos \theta, \sin \theta) lie on the circle.

  • Sine and cosine are periodic functions with period 2π2\pi.

  • The trigonometric circle helps visualize the signs and values of sine and cosine in all four quadrants.