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Unit Circle Calculator

Find sine, cosine, tangent, and unit circle coordinates for any angle. Enter an angle in degrees or radians and get accurate trigonometric results instantly.

Calculate Unit Circle Values

Enter an angle and choose your preferred unit.

Unit Circle Result

Radians 0
Cosine (x) 0
Sine (y) 0
Tangent 0

Unit Circle Formula

The unit circle is a circle centered at the origin with a radius of 1. Every point on the unit circle can be represented using its x and y coordinates, which correspond to cosine and sine values.

Unit Circle Equation
x² + y² = 1

For an angle θ, the coordinates of a point on the unit circle are (cos θ, sin θ). Therefore, cosine represents the x-coordinate and sine represents the y-coordinate.

Coordinate Formula
(x, y) = (cos θ, sin θ)

How Does the Unit Circle Calculator Work?

This calculator converts your angle into radians when necessary and then uses standard trigonometric functions to determine the corresponding unit circle values.

1

Enter an Angle

Enter your angle value in degrees or radians.

2

Choose the Unit

Select degrees or radians depending on the angle you entered.

3

View Results

Get radians, cosine, sine, tangent, and unit circle coordinates instantly.

Common Unit Circle Angles

These angles are frequently used in trigonometry and are useful for memorizing important unit circle values.

0 radians
30° π / 6
45° π / 4
60° π / 3
90° π / 2
180° π
270° 3π / 2
360°

What Is the Unit Circle?

The unit circle is a fundamental concept in trigonometry. It has a radius of exactly one unit and is centered at the origin of a coordinate plane.

The unit circle helps define the relationships between angles and trigonometric functions. For any angle θ, the x-coordinate of the corresponding point represents cos θ, while the y-coordinate represents sin θ.

Understanding Sine, Cosine, and Tangent

Frequently Asked Questions

What is a unit circle?
A unit circle is a circle centered at the origin with a radius of exactly one unit. It is widely used to understand trigonometric functions.
What are the coordinates on a unit circle?
For an angle θ, the coordinates are (cos θ, sin θ), where cosine is the x-coordinate and sine is the y-coordinate.
What is the unit circle equation?
The standard equation of a unit circle is x² + y² = 1.
What is sin 90 degrees?
The sine of 90 degrees is exactly 1.
What is cos 0 degrees?
The cosine of 0 degrees is exactly 1.
Can I enter negative angles?
Yes. The calculator supports negative angles as well as angles greater than 360 degrees.