Trig Tour: free math simulation
Drag a point around the unit circle and trace sin, cos and tan.
▶ Open the simulationFree, no sign-up. Works on phones, tablets and laptops.
The science
On a circle of radius 1, the point at angle θ has coordinates (cos θ, sin θ). Tangent is the ratio sin θ / cos θ. Tracing these values as the angle grows produces the familiar sine and cosine waves.
sin²θ + cos²θ = 1
Things to try
- Find the angles where sin θ = cos θ.
- Read off sin, cos and tan at 30°, 45° and 60°.
- Watch tan θ shoot to infinity at 90°.
Topics covered
unit circle sine cosine tangent radians degrees
How to use it
Open the simulation, then change the experiment live with the sliders, checkboxes and buttons in the side panel. Drag objects on screen where it makes sense, and use Pause, Step, Speed and Reset in the bottom bar to study every moment.
Frequently asked questions
What does the Trig Tour simulation show?
On a circle of radius 1, the point at angle θ has coordinates (cos θ, sin θ). Tangent is the ratio sin θ / cos θ. Tracing these values as the angle grows produces the familiar sine and cosine waves.
What is the key equation?
sin²θ + cos²θ = 1
Is the Trig Tour simulation free?
Yes. It runs free in any web browser on phones, tablets and laptops, with no sign-up or download.
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