Definition: The amplitude of a sine or cosine graph is half the distance between its maximum and minimum values, equal to the absolute value of the coefficient A.
What is amplitude?
For y = A sin(Bx) or y = A cos(Bx), the amplitude is |A|. It measures how far the wave rises above, and falls below, its midline. Equivalently, it is (maximum – minimum) / 2.
How do you find it?
Worked example: a tide model has high water at 9.4 feet and low water at 1.2 feet. The amplitude is (9.4 – 1.2)/2 = 4.1 feet. The midline sits at (9.4 + 1.2)/2 = 5.3 feet, so one model is h(t) = 4.1 cos(Bt) + 5.3.
If A is negative, as in y = -3 sin x, the amplitude is still 3; the negative sign reflects the graph over the x-axis.
What mistake is common?
Reporting the full height from bottom to top instead of half of it. Another is giving a negative amplitude. Mathbot says amplitude is a distance, so it is never negative.
Where to learn it
- Graphing Waves: Sine and Cosine Models – lesson
- Graphing Sine, Cosine and Tangent Functions – lesson