Math & Algebra Tool
Unit Circle Chart
Interactive trigonometry reference.
Trig Values at 45°
Radians0.785π
Cos(θ) / X0.707
Sin(θ) / Y0.707
Tan(θ)1.000
Click coordinates on the circle to snap to common angles.
Frequently Asked Questions
What is a Unit Circle?+
A unit circle is a circle with a radius of exactly 1, centered at (0,0) on the Cartesian coordinate system. It is a fundamental tool in trigonometry for defining sine and cosine functions.
Why is the radius 1?+
A radius of 1 simplifies calculations. In a right triangle with hypotenuse 1, the adjacent side equals Cos(θ) and the opposite side equals Sin(θ) directly.
What are Radians?+
Radians are a way of measuring angles based on the radius. One radian is the angle where the arc length equals the radius. A full circle (360°) corresponds to 2π radians.
How do I convert Degrees to Radians?+
Multiply the degrees by π/180. For example, 90° × π/180 = π/2 radians.
What coordinates represent Cosine and Sine?+
On the unit circle, any point (x, y) corresponds to (Cos θ, Sin θ). The x-coordinate represents the cosine of the angle, and the y-coordinate represents the sine.
Why is Tangent undefined at 90° and 270°?+
Tangent is defined as Sin(θ) / Cos(θ). At 90° and 270°, Cos(θ) is 0. Division by zero is undefined, so the tangent function has vertical asymptotes at these angles.