Unit Circle Calculator
Enter an angle to find trig values and unit circle coordinates.
Trig Values
| Property | Value |
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Standard Angles Reference
| Degrees | Radians | sin | cos | tan |
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Request a ToolHow to Use the Unit Circle Calculator
This calculator finds the exact position and trig values for any angle on the unit circle.
- Enter an angle. Type any angle value, including negative numbers or values larger than 360 degrees.
- Choose degrees or radians. The calculator converts between both automatically and shows both in the results.
- Read the results. The (x, y) coordinates on the unit circle are displayed along with sin, cos, tan, and the quadrant. The reference table below shows values for all standard angles.
About the Unit Circle
The unit circle is a circle with radius 1 centered at the origin of a coordinate plane. For any angle measured from the positive x-axis, the point where the terminal side intersects the unit circle has coordinates (cos, sin). This provides a geometric definition of sine and cosine that extends beyond right triangles to all angles. Tangent equals the y-coordinate divided by the x-coordinate (sin/cos). The standard angles (0, 30, 45, 60, 90 degrees and their equivalents in other quadrants) have exact values involving square roots that students memorize for tests and practical use.
Frequently Asked Questions
What are the unit circle coordinates?
For any angle theta on the unit circle, the coordinates of the corresponding point are (cos(theta), sin(theta)). The x-coordinate equals cosine and the y-coordinate equals sine. This definition works for all angles, not just acute angles.
What are the standard angles on the unit circle?
The standard angles are 0, 30, 45, 60, 90, 120, 135, 150, 180, 210, 225, 240, 270, 300, 315, and 330 degrees. These correspond to angles with exact trig values involving fractions and square roots. The reference table in this calculator shows all of them.
How do quadrants affect trig function signs?
In Quadrant I (0-90 degrees), all trig functions are positive. In Quadrant II (90-180), only sine is positive. In Quadrant III (180-270), only tangent is positive. In Quadrant IV (270-360), only cosine is positive. A common mnemonic is "All Students Take Calculus" for the positive functions in each quadrant.