Browser-local angle arithmetic

Unit Circle Calculator

Map an angle to normalized unit-circle coordinates with quadrant and reference context.

Calculate

Enter values and calculate.

Formula and method

On the unit circle, x = cos θ and y = sin θ. The tool also reports normalization, quadrant or axis, reference angle, and tangent when defined.

Worked example

30° maps numerically to approximately (0.866025403784, 0.5). At 90°, tangent is reported as undefined.

Limits and ownership boundary

This is a dedicated angle-to-coordinate workflow, not a general scientific calculator. Numeric output is used; exact radicals are not guessed from floating-point values.

Method source

OpenStax Precalculus 2e: Angles and Unit Circle: Sine and Cosine.