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

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
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Solution

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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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