Math
Unit circle.
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
Real-world.
- 1 At θ = 0°, the point on the unit circle is (1, 0), so cos(0°) = 1 and sin(0°) = 0
- 2 At θ = 90°, the point is (0, 1), so cos(90°) = 0 and sin(90°) = 1
- 3 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
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