AISL 2.5.8 Creating a sinusoidal model

In this lesson, the focus is on creating a sinusoidal model to represent the depth of water in a harbor based on tidal changes. The model is derived from given data: at low tide, the water depth is 2 meters, and at high tide, 6.8 meters, occurring 6 hours later.

Key points include:

• The period of the function is determined to be 12 hours, as it takes 6 hours to reach high tide and another 6 hours to return to low tide.
• The equation is formulated as $D = -2.4 \cos(30T) + 4.4$, where:
  • The amplitude $A$ is calculated as (with a negative sign since it starts at the minimum).