Sine graphs are really important for understanding how waves work in math, especially in trigonometry.

Amplitude

• What It Is: The amplitude of a sine wave tells us how far the wave goes up and down from its middle point.
• Example: If we have the formula (y = A \sin(x)), the amplitude is the absolute value of (A). So, if (A = 2), the graph will go up to 2 and down to -2.

Periodicity

• What It Is: The period of a sine wave is how long it takes to complete one full wave cycle.
• Example: For the regular sine function (y = \sin(x)), the period is (2\pi). This means that the wave repeats itself every (2\pi) units along the x-axis. If we change the function to (y = \sin(2x)), the period gets cut in half to (\pi).

Summary

In short, by looking at a sine graph, you can see how amplitude changes the height of the wave. The periodicity shows us how the wave keeps repeating over and over again.