What is the unit circle?

The unit circle is a circle with radius 1 centered at the origin (0, 0). It's used to define trigonometric functions for all angles.

How do I read coordinates from the unit circle?

For any angle θ, the x-coordinate is cos(θ) and the y-coordinate is sin(θ). The point (cos(θ), sin(θ)) lies on the unit circle.

⭕ Unit Circle Calculator

Explore the unit circle interactively: angles → (x, y), sin, cos, tan.

Unit Circle Calculator

Angle

Coordinates (x, y)

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Quadrant

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sin(θ)

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cos(θ)

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tan(θ)

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Reference Angle

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The unit circle is a circle with radius 1 centered at the origin. It's fundamental to trigonometry because the coordinates of any point on the unit circle are (cos(θ), sin(θ)), where θ is the angle. Our interactive unit circle calculator lets you explore angles and see their corresponding coordinates and trigonometric values.

Key Points

Important angles on the unit circle.

0°: (1, 0)

At 0°, cos = 1, sin = 0.

90°: (0, 1)

At 90°, cos = 0, sin = 1.

180°: (-1, 0)

At 180°, cos = -1, sin = 0.

270°: (0, -1)

At 270°, cos = 0, sin = -1.

Use Cases

Common applications of the unit circle.

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Education

Understanding trigonometric functions
Learning angle relationships
Visualizing sin and cos

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Problem Solving

Finding exact trigonometric values
Understanding quadrants
Working with reference angles

Frequently Asked Questions

Common questions about the unit circle.

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Last updated: 2025-10-21 — Compiled and reviewed by Calvin (Math Research, FreeCalculators.app)