Amplitude and Midline

Every sinusoid wobbles above and below some horizontal center line. That center line is the midline, and it tells you where the wave is balanced, not how far it swings. The amplitude tells you the swing: how far the curve reaches above the midline, which is the same as how far it dips below. Together they describe the whole vertical behavior of the wave, while frequency and phase shift (covered elsewhere) handle the horizontal behavior.

To build both numbers from a graph or a table, you only need the maximum value and the minimum value. The midline sits exactly halfway between them, so midline D equals (max + min) divided by 2. The amplitude is half the total vertical distance the wave covers, so A equals (max - min) divided by 2. Once you have A and D, you can write the equation y = A sin(x) + D or y = A cos(x) + D, matching whichever starting behavior the wave shows.

This matters because a sinusoid's maximum value is not a clean, standalone feature. It is really the midline plus the amplitude, two separate ideas tangled into one number. Separating them is what lets you compare waves fairly: two waves can have the same maximum but completely different amplitudes if their midlines differ. This separation also sets up later work on transformations, where sliding a wave up or down changes only D, while stretching it vertically changes only A.