Graph of y = sin(x)
The sine graph is a smooth wave that repeats every 2π (period), stays between −1 and 1 (amplitude 1), and crosses zero at every multiple of π.
At a glance
| What it is | Graph y = sin(x) online. Learn the period 2π, amplitude and phase shift, and drag sliders in y = a·sin(bx) to see them change. Free. |
|---|---|
| Type | Interactive guide with a calculator |
| Level | High school and college |
| Price | Free, with no account or sign-up |
| Works offline | Yes, after the first visit; installs as an app |
| Made by | Aalok (aalok.builds@gmail.com) |
| Last updated | 1 November 2026 |
Key facts
| Period | 2π ≈ 6.283 (360°) |
|---|---|
| Amplitude | 1 |
| Range | −1 ≤ y ≤ 1 |
| Zeros | x = 0, ±π, ±2π, … |
| Maximum | 1 at x = π/2 + 2πn |
| y = A·sin(Bx + C) + D | Amplitude |A|, period 2π ÷ |B|, vertical shift D |
What are amplitude and period?
In y = a·sin(bx), a stretches the wave vertically (a = 3 swings between −3 and 3) and b squeezes it horizontally, so the period becomes 2π ÷ b. Drag the sliders above to see both effects.
How to use it in Plotline
- The graph of y = a·sin(bx) with sliders for a and b is already loaded above. Edit the equation in the list to change it.
- Drag the graph to move around, scroll or pinch to zoom, and tap the crosshair to reset the view.
- Hover over or tap the curve to read the coordinates of any point.
- Press Enter to add another equation and compare graphs in different colors.
Frequently asked questions
What is the period of sin(2x)?
π. The period of sin(bx) is 2π ÷ b, so doubling b from 1 to 2 halves the period from 2π to π. Drag the b slider above to watch the wave squeeze together as b grows.
Does the calculator use degrees or radians?
The graph uses radians, so one full wave spans 2π ≈ 6.28 along the x-axis. The scientific calculator has its own degrees/radians switch, so you can work in degrees there when a question asks for them.
Is it free?
Yes. The graphing calculator is free with no account and no sign-up: plot as many equations as you like, use sliders, save graphs in your browser and share them by link. It installs as an app and keeps working offline.
Learn more
Related
- Cosine graph – Graph y = cos(x) online and compare it with sin(x).
- Tangent graph – Graph y = tan(x) online.
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Plotline is an independent project and is not affiliated with Desmos, Texas Instruments or Casio.