Sine & Cosine Wave Explorer: Amplitude, Period, Phase
Shape y = A sin(B(x - C)) + D by dragging handles on the graph and see each change in the equation.
Shape the wave y = A sin(B(x − C)) + D. Drag the colored handles on the graph: the red one changes the amplitude, the blue one the period, the green one the phase shift and the purple one the midline.
About the Sine & Cosine Wave Explorer: Amplitude, Period, Phase
Free sine & cosine wave explorer: amplitude, period, phase. Shape y = A sin(B(x - C)) + D by dragging handles on the graph and see each change in the equation. Drag, change the sliders and see the result live. No sign-up, works on phone and computer. Built for math, the sine & cosine wave explorer: amplitude, period, phase 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.
Shape y = A sin(B(x - C)) + D by dragging handles on the graph and see each change in the equation. 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 Sine & Cosine Wave Explorer: Amplitude, Period, Phase
- Use the controls to change Function, Amplitude A, Period, Phase shift C, Midline D, and more. The simulation reacts instantly.
- Pick an option such as sine, cosine, Show, Hide to switch modes or load an example.
- Press "Reset to y = sin x" 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
- Double the amplitude and watch the highest and lowest values.
- Set the period to π and see the equation change.
- Shift a sine wave by π/2 and match it to cosine.
- Raise the midline to 2 and read the new highest and lowest values.
Key ideas you can learn
- Amplitude is the height of the wave from the midline.
- Period is the length of one full cycle, and frequency is 1 divided by the period.
- Phase shift moves the wave left or right.
- The midline moves the whole wave up or down.
Where this is used in the real world
Sound, light, tides, AC electricity, seasons and music are all modeled by sine waves with different amplitude, period and phase.
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 is a cosine graph related to a sine graph?
A cosine wave is a sine wave shifted left by a quarter of a period.
How do you find the period from B?
Period = 2π ÷ B, so a bigger B means a shorter period.
Is the Sine & Cosine Wave Explorer: Amplitude, Period, Phase 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 Sine & Cosine Wave Explorer: Amplitude, Period, Phase 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.