Explore the Sine & Cosine Wave Explorer: Amplitude
Shape y = A sin(B(x - C)) + D by dragging handles on the graph and see each change in the equation. 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 Sine & Cosine Wave Explorer: Amplitude with sample data entered and the result showing.
What is the Sine & Cosine Wave Explorer: Amplitude?
Shape y = A sin(B(x - C)) + D by dragging handles on the graph and see each change in the equation. It runs in your browser, so a change to a setting or a drag on an object shows up at once.
Sound, light, tides, AC electricity, seasons and music are all modeled by sine waves with different amplitude, period and phase.
3 steps to your result
Open the tool and follow along. Nothing to install.
What you get
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.
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.
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 Sine & Cosine Wave Explorer: Amplitude, Period, Phase on the board, let students predict the result, then run it together and test this: Set the period to π and see the equation change. 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 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. The Sine & Cosine Wave Explorer: Amplitude, Period, Phase 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 Sine & Cosine Wave Explorer: Amplitude, Period, Phase work on a phone or tablet?
Yes. The Sine & Cosine Wave Explorer: Amplitude, Period, Phase takes touch input as well as mouse input, so you can use its 6 adjustable settings with a finger. A larger screen makes the controls and graphs easier to read.
How do I use the Sine & Cosine Wave Explorer: Amplitude?
1. In 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. 2. In the Sine & Cosine Wave Explorer: Amplitude, Period, Phase, pick an option such as sine, cosine, Show, Hide to switch modes or load an example. 3. In the Sine & Cosine Wave Explorer: Amplitude, Period, Phase, press "Reset to y = sin x" to start, reset or change what is happening. 4. Start with this experiment: Double the amplitude and watch the highest and lowest values. Drag any glowing handle, object or slider with your mouse or finger and the Sine & Cosine Wave Explorer: Amplitude, Period, Phase responds in real time. 5. Change one setting at a time and watch which readout moves, then compare it with this idea: Amplitude is the height of the wave from the midline.
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Try the Sine & Cosine Wave Explorer: Amplitude now
Shape y = A sin(B(x - C)) + D by dragging handles on the graph and see each change in the. Free to use.
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