Graphing calculator example
See how amplitude changes a sine graph
In y = a sin(x), multiplying by a changes the height of the wave. This example uses radians. Select a table row to see the corresponding point, then change a.
Try it on the graph
y = a sin(x)
Solid: current graph. Dashed: starting graph. Axes use the labeled scales.
| x | y |
|---|---|
| 0 | |
| -1 | |
| 0 | |
| 1 | |
| 0 |
Values are rounded to seven significant digits. Tiny sine rounding errors display as 0.
Work one row: a = 2 and x = π/2
- The sine of π/2 radians is 1.
- Substitute into y = 2 sin(x): y = 2 × 1 = 2.
- The point is (π/2, 2). At x = −π/2 the sine is −1, so the output is −2.
What to notice
The amplitude is |a|. A negative a reflects the graph across the x-axis; the amplitude itself is never negative.
For nonzero a, this wave repeats every 2π radians. Changing a does not change that period.
At a = 0, every output is 0. The graph is constant rather than an oscillating wave.
Check your understanding
Set a = −2. At x = π/2, the output is −2. At x = −π/2, it is 2. The wave has flipped, while its amplitude remains 2.
Keep exploring
The full calculator lets you edit equations, add more curves, set axis bounds, and share or export your graph. The examples here use ordinary real-number arithmetic; graph lines and computed values are numerical approximations.
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