Unit Circle
Explore the unit circle with this interactive tool. See sin, cos, and tan values for any angle with a visual diagram and reference table.
About Unit Circle
The unit circle is a foundational concept in trigonometry. This interactive tool gives you a visual, clickable diagram that makes it easy to understand how angles relate to sine, cosine, and tangent values.
Interactive Visualization
Click anywhere on the circle or pick a standard angle to see the corresponding point highlighted. Color-coded lines show the cosine (blue), sine (red), and tangent (green) components. The coordinates of the point are displayed in exact form using fractions and square roots where possible.
Standard Angles and Exact Values
All 16 standard angles from 0 to 330 degrees are marked on the circle. The reference table at the bottom shows every standard angle with its radian equivalent and exact trig values, so you can study or verify your answers quickly. Click any row in the table to jump to that angle on the diagram.
Degrees and Radians
Enter an angle in degrees and the tool displays the radian equivalent instantly. Standard angles are shown as neat fractions of pi. For further calculations, try the Graphing Calculator to plot trig functions, or the Scientific Calculator for evaluating expressions. All processing happens in your browser with nothing sent to any server.
Frequently Asked Questions
What is the unit circle?
The unit circle is a circle with a radius of 1 centered at the origin (0, 0). It's a key concept in trigonometry because the x-coordinate of any point on the circle equals the cosine of the angle, and the y-coordinate equals the sine.
How do I use this tool?
Click anywhere on the circle to set an angle, use the degree input to type a specific value, or click one of the standard angle buttons (0, 30, 45, 60, 90, etc.) for exact values. The tool instantly shows sin, cos, and tan along with the angle in radians.
What are the standard angles on the unit circle?
Standard angles are the commonly memorized angles: 0, 30, 45, 60, 90, 120, 135, 150, 180, 210, 225, 240, 270, 300, 315, and 330 degrees. Their trig values involve simple fractions and square roots.
What do the colored lines mean?
Blue represents cosine (the horizontal projection), red/rose represents sine (the vertical projection), and green represents the tangent line. These colors match the value cards below the circle.
When is tangent undefined?
Tangent is undefined at 90 and 270 degrees (and their equivalents) because you'd be dividing by zero. At these angles, cosine equals zero and tan = sin/cos would require division by zero.