What is the sine wave formula in terms of A, B, C, and D?

The correct representation of a sine wave incorporates the parameters A, B, C, and D in a specific structure that represents amplitude, frequency, phase shift, and vertical shift respectively. The formula y = A sin(Bx + C) + D captures these components effectively.

In this formula:

• A represents the amplitude of the sine wave. It dictates the height of the peaks and the depth of the troughs from the centerline, thus determining how "tall" or "short" the wave appears.

• B influences the frequency of the sine wave. It determines how many cycles the wave completes in a given interval, effectively stretching or compressing the wave horizontally.

• C is associated with the phase shift of the sine wave. It indicates how much the wave is shifted horizontally from its standard position. Positive values of C shift the wave to the left, while negative values shift it to the right.

• D signifies the vertical shift of the wave. It moves the entire sine wave up or down on the graph, altering the midline around which the wave oscillates.

This structure makes the formula A sin(Bx + C) + D the most comprehensive choice that correctly represents a sine wave in terms of these parameters. The other options either