Unit Circle Calculator

Use the Unit Circle Calculator for a transparent, instant calculation with validated inputs and cited sources. For a query such as “trig circle”, enter the matching values and units below and review the stated assumptions.

Inputs

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Result

Results update as you type.

Cosine / x
0.5
Sine / y
0.8660254038
Equivalent angle in [0, 2π)
1.0471975512

How to use this calculator

Enter the requested values and units.

Review the assumptions and any warnings shown with the result.

Use the result together with the cited source and your real-world requirements.

Formula

Reduce the entered degree angle modulo 360, convert that equivalent angle to radians in [0, 2π), and return the unit-circle coordinates (cos θ, sin θ).

Worked example

Worked example: Inputs: Angle: 60 °. Outputs: Cosine / x: 0.5; Sine / y: 0.866025; Equivalent angle in [0, 2π): 1.047198.

Assumptions and limits

  • The result depends on the values, units, and assumptions entered. It does not infer missing context.

Sources

Related calculators

Frequently asked questions

How does the Unit Circle Calculator work?

Reduce the entered degree angle modulo 360, convert that equivalent angle to radians in [0, 2π), and return the unit-circle coordinates (cos θ, sin θ).

What should I enter?

Angle

What should I verify?

Review the assumptions and any warnings shown with the result. The result depends on the values, units, and assumptions entered. It does not infer missing context.

Last updated 2026-08-14 · math-unit-circle-v1 · opportunity-content-2026-08-14 · Trusty Calculator Editorial Team