What does the equation y = A sin(Bx + C) + D represent mathematically?

The equation ( y = A \sin(Bx + C) + D ) represents a sine function due to its structure.

In this equation, the term ( \sin(Bx + C) ) is indicative of the sine wave, which is a fundamental periodic function that oscillates between -1 and 1. The parameters ( A ), ( B ), ( C ), and ( D ) modify the characteristics of the sine wave:

• The parameter ( A ) represents the amplitude of the sine wave, which determines how tall the wave appears from its midline (central axis).

• The parameter ( B ) influences the frequency of the wave, dictating how many cycles occur over a given interval. Specifically, frequency is related to the period of the wave, which is calculated as ( \frac{2\pi}{B} ).

• The parameter ( C ) represents a phase shift, which shifts the wave left or right along the x-axis.

• The parameter ( D ) adjusts the vertical position of the wave, effectively shifting it up or down.

These properties underpin the behavior of the sine function and highlight why the equation is classified as representing a sine function. In contrast, other types of