Today we will explore how the parameter A affects the graph of y equals A sine of omega x plus phi. The amplitude A controls the vertical stretching of the sine function. Let's start by examining the standard sine function y equals sine x, which has an amplitude of 1.
When A is greater than 1, the sine function undergoes vertical stretching. For A equals 2, the amplitude doubles to 2, making the wave twice as tall. For A equals 3, the amplitude becomes 3. Notice how the period remains unchanged, but the maximum and minimum values increase proportionally with A.
When A is between 0 and 1, the sine function undergoes vertical compression. For A equals 0.5, the amplitude is halved, making the wave half as tall. For A equals 0.25, the amplitude becomes one quarter of the original. The wave becomes increasingly flatter as A approaches zero, but the period remains constant.
Now let's see the dynamic effect of changing A. As A increases from 0.5 to 3, the sine wave stretches vertically, reaching higher peaks and lower valleys. When A decreases back to 0.5, the wave compresses. The dashed lines show the amplitude boundaries, demonstrating how A directly controls the maximum displacement from the x-axis.