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Trigonometry · Unit circle

Exact Trigonometric Values & Identities Calculator

Find sine, cosine, and tangent for angles from 0° to 360°, including exact radical forms for common unit-circle angles.

Formula shown Runs locally Reviewed Aug 11, 2026
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Equation guide

Unit-circle values for angles from 0° through 360°

Coordinates

P=(cos θ, sin θ)

Fundamental identity

sin²θ+cos²θ=1

Tangent

tan θ=sin θ/cos θcos θ≠0
Trigonometry · Unit circle

Connect exact and decimal trigonometric values

Exact radical forms are available for standard unit-circle angles. Other angles receive decimal values only.

Inputs and displayed decimal results use at most three decimal places. Exact internal values are retained during calculation.

sin²θ + cos²θ = 1

Choose a common angle or enter a custom angle from 0° through 360°.

θ

Using the model

Symbols, assumptions and limitations

Interpretation notes

Angles are entered in degrees and converted internally to radians. Exact forms are shown for standard multiples of 30° and 45°. Tangent is undefined where cosine is zero.

Worked examples

See the method in practice

01

Angle 45°

At 45°, sine and cosine both equal √2/2, tangent equals 1, and the point lies in quadrant I.

02

Angle 150°

At 150°, sine is 1/2, cosine is −√3/2, and tangent is −√3/3.

Questions

Frequently asked

Why is tangent undefined at 90° and 270°?

Tangent is sin θ divided by cos θ, and cosine is zero at those angles.

Why show exact and decimal values?

Exact forms preserve the mathematical structure; decimals help with numerical comparison and applications.

What does the unit-circle point mean?

Its horizontal coordinate is cos θ and its vertical coordinate is sin θ.

Sources & review

Equations and examples are checked against the references below. Results are educational and should be independently verified for safety-critical work.

OpenStax Precalculus — Unit Circle

Written by the STEM Hub editorial team · Reviewed August 11, 2026 · Review methodology