Unit Circle & Trig Explorer
Drag around the unit circle and watch sine, cosine and tangent trace their waves.
About the Unit Circle & Trig Explorer
Free interactive unit circle. Drag the angle in degrees or radians and see sin, cos and tan values plus live sine and cosine waves. Perfect for trigonometry students. Built for math, the unit circle & trig explorer runs instantly in your browser: change a setting or drag an object and the result updates at once, so you learn by trying things out rather than only reading about them.
Drag around the unit circle and watch sine, cosine and tangent trace their waves. Use it to explore math ideas at your own pace, then check what you found against the key ideas further down this page.
How to use the Unit Circle & Trig Explorer
- Use the controls to change θ, Special angles. The simulation reacts instantly.
- Pick an option such as 0, π/6, π/4, π/3 to switch modes or load an example.
- Press "Animate" to start, reset or change what is happening.
- Where you see a glowing handle, object, weight or atom, drag it with your mouse or finger. Everything responds in real time.
- Watch the readouts and graphs update as you experiment, and compare what you see with the key ideas below.
Things to try
- Drag to 30°, 45° and 60° and read the values.
- Watch the sine wave trace as you animate.
- Find where tan is undefined.
- Convert 135° to radians.
Key ideas you can learn
- On the unit circle a point at angle θ has coordinates (cos θ, sin θ).
- Radians measure the arc length: 180° = π radians.
- Unrolling the circle over time gives the sine and cosine waves.
Where this is used in the real world
The unit circle underlies sound waves, alternating current, computer graphics, rotation in games and GPS calculations.
Who is this simulation for?
Algebra, geometry, trigonometry and calculus students, teachers preparing demonstrations, and self-learners who want to see the maths move.
For teachers: project it on the board, let students predict what will happen, then run it together. For students: change one thing at a time and write down what changes.
Frequently asked questions
How do I convert degrees to radians?
Multiply by π / 180. For example 90° = π/2 radians and 180° = π radians.
Why is tan undefined at 90 degrees?
Tangent is sin ÷ cos, and cos 90° = 0, so you would divide by zero.
Is the Unit Circle & Trig Explorer free to use?
Yes. It is completely free, with no signup, no download and no ads inside the simulation. It runs in your web browser.
Does the Unit Circle & Trig Explorer work on a phone or tablet?
Yes. It uses touch as well as the mouse, so you can drag objects with your finger. A larger screen makes the controls easier to see.