Unit Circle Calculator
Find sine, cosine, and tangent values for any angle in degrees or radians with our interactive unit circle calculator. Visualize angles and coordinates on the unit circle to better understand trigonometric functions.
Your Results
| Angle in Degrees | 0° |
|---|---|
| Angle in Radians | 0 rad |
| Reference Angle | 0° |
| Quadrant | - |
Trigonometric Values:
| Function | Value |
|---|---|
| sin(θ) | 0 |
| cos(θ) | 0 |
| tan(θ) | 0 |
| csc(θ) | - |
| sec(θ) | - |
| cot(θ) | - |
Coordinates on Unit Circle:
| X Coordinate (cos) | 0 |
|---|---|
| Y Coordinate (sin) | 0 |
About the Unit Circle Calculator
The unit circle is a fundamental concept in trigonometry that provides a geometric representation of trigonometric functions. It's a circle with a radius of 1 centered at the origin (0,0) in the coordinate plane. The unit circle allows us to define sine, cosine, and tangent for all real numbers.
How the Unit Circle Works
On the unit circle:
- The x-coordinate of a point on the circle represents the cosine of the angle
- The y-coordinate represents the sine of the angle
- The tangent of the angle is the ratio of y-coordinate to x-coordinate (sin/cos)
- Angles are measured from the positive x-axis, with positive angles going counterclockwise
Key Features of the Unit Circle
The unit circle has several important properties:
- Quadrants: The circle is divided into four quadrants, each representing a 90° (π/2 radians) range
- Reference Angles: For any angle, the reference angle is the acute angle it makes with the x-axis
- Periodicity: Trigonometric functions are periodic, repeating every 360° (2π radians)
- Symmetry: The circle has symmetry that allows us to find values for angles in different quadrants
Common Unit Circle Values
Here are some important angles and their trigonometric values:
| Angle (Degrees) | Angle (Radians) | sin(θ) | cos(θ) | tan(θ) |
|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 |
| 30° | π/6 | 1/2 | √3/2 | √3/3 |
| 45° | π/4 | √2/2 | √2/2 | 1 |
| 60° | π/3 | √3/2 | 1/2 | √3 |
| 90° | π/2 | 1 | 0 | undefined |
Using the Unit Circle Calculator
Our calculator helps you:
- Convert between degrees and radians
- Find trigonometric function values for any angle
- Determine the reference angle and quadrant
- Visualize the angle and its coordinates on the unit circle
- Understand the relationships between different trigonometric functions