Explore the Unit Circle & Trig Explorer
Drag around the unit circle and watch sine, cosine and tangent trace their waves. Free, no signup, runs in your browser.
- Free to use
- No signup
- Nothing to install
- Runs in your browser
Illustration. Open the tool for the real thing.
See it in action
The Unit Circle & Trig Explorer with sample data entered and the result showing.
What is the Unit Circle & Trig Explorer?
Drag around the unit circle and watch sine, cosine and tangent trace their waves. It runs in your browser, so a change to a setting or a drag on an object shows up at once.
The unit circle underlies sound waves, alternating current, computer graphics, rotation in games and GPS calculations.
3 steps to your result
Open the tool and follow along. Nothing to install.
What you get
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.
Drag to 30°, 45° and 60° and read the values.
Watch the sine wave trace as you animate.
Find where tan is undefined.
Used for
Pick one to see how it fits.
Math learners
Algebra, geometry, trigonometry and calculus students, teachers preparing demonstrations, and self-learners who want to see the maths move.
Try it freeTeachers
For teachers: project the Unit Circle & Trig Explorer on the board, let students predict the result, then run it together and test this: Watch the sine wave trace as you animate. For students: change one thing at a time and write down what changes.
Try it freeHow it compares
A plain look at this tool next to the usual alternative.
| This simulation | Textbook diagram | |
|---|---|---|
| Interactive | Drag, tap and change settings | Fixed picture |
| Install | Nothing to install | Not needed |
| Cost | Free to use | Depends on the book |
Questions people ask
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. The Unit Circle & Trig Explorer is free, needs no signup or download and runs in your web browser. It is part of the Math group of AZRS simulations.
Does the Unit Circle & Trig Explorer work on a phone or tablet?
Yes. The Unit Circle & Trig Explorer takes touch input as well as mouse input, so you can use its 2 adjustable settings with a finger. A larger screen makes the controls and graphs easier to read.
How do I use the Unit Circle & Trig Explorer?
1. In the Unit Circle & Trig Explorer, use the controls to change θ, Special angles. The simulation reacts instantly. 2. In the Unit Circle & Trig Explorer, pick an option such as 0, π/6, π/4, π/3 to switch modes or load an example. 3. In the Unit Circle & Trig Explorer, press "Animate", "Reset to 0°" to start, reset or change what is happening. 4. Start with this experiment: Drag to 30°, 45° and 60° and read the values. Drag any glowing handle, object or slider with your mouse or finger and the Unit Circle & Trig Explorer responds in real time. 5. Change one setting at a time and watch which readout moves, then compare it with this idea: On the unit circle a point at angle θ has coordinates (cos θ, sin θ).
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Try the Unit Circle & Trig Explorer now
Drag around the unit circle and watch sine, cosine and tangent trace their waves. Free to use.
Try it free