Unit Circle Calculator

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Explore trigonometric values (sin, cos, tan) on the unit circle.

Angle Specification

Angle (θ)

Common Points

0° (0 rad)(1, 0)

90° (π/2)(0, 1)

180° (π)(-1, 0)

270° (3π/2)(0, -1)

Trig Coordinates

(0.707, 0.707)

Intersection (x, y)

Coordinates of the intersection point on the unit circle.

Cosine (x)0.7071

Sine (y)0.7071

Tangent (y/x)1.0000

Cosine (x)

Sine (y)

About this calculator

What is the Unit Circle?

The unit circle is a circle with a radius of 1, centered at the origin (0, 0) in the Cartesian coordinate system. It is a fundamental tool in trigonometry used to relate angles to coordinates. For any angle θ, the point where the terminal side intersects the unit circle has coordinates (cos θ, sin θ).

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Pro Tips

The x-coordinate is always the Cosine and the y-coordinate is always the Sine.
The Unit Circle is divided into four quadrants (I, II, III, IV) where signs of sin/cos change.
Special angles like 30°, 45°, and 60° have exact radical values (e.g., √3/2).

Fun Facts

"The unit circle allows trigonometric functions to be defined for all real numbers, not just acute angles in triangles."
"The word 'sine' comes from the Latin 'sinus', meaning 'bay' or 'fold', translating from Arabic 'jiba'."
"Tangent is named 'tangent' because it's the length of a segment on a line tangent to the circle."

Formula: x² + y² = 1 | x = cos(θ), y = sin(θ)