Questions: In the equation (y=A sin (B(x-C))+D), what does (D) determine? vertical shift horizontal (or phase) shift amplitude period

Transcript text: In the equation $y=A \sin (B(x-C))+D$, what does $D$ determine? vertical shift horizontal (or phase) shift amplitude period

Solution

Solution Steps

The parameter $ D $ in the equation $ y = A \sin(B(x - C)) + D $ determines the vertical shift of the sine wave. It shifts the entire graph of the sine function up or down by $ D $ units.

Step 1: Identify the Role of $ D $ in the Equation

In the equation $ y = A \sin(B(x - C)) + D $, the parameter $ D $ represents the vertical shift of the sine wave. This means that the entire graph of the sine function is shifted up or down by $ D $ units.

Step 2: Apply the Vertical Shift

Given $ D = 3 $, the sine wave is shifted vertically by 3 units. This means that every point on the graph of the sine function is moved 3 units upwards.

Final Answer

The vertical shift is $ \boxed{3} $ units.

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