he graph of y = A sin Bx has amplitude = and period=

For the function \( y = A \sin(Bx) \), the **amplitude** and **period** are determined by the constants \( A \) and \( B \).

1. **Amplitude**: The amplitude is the absolute value of \( A \), which represents the maximum vertical distance from the centerline of the graph to the peak (or trough) of the wave. 

   \[
   \text{Amplitude} = |A|
   \]

2. **Period**: The period is the horizontal length of one complete cycle of the sine wave. It is calculated using the formula:

   \[
   \text{Period} = \frac{2\pi}{|B|}
   \]

### Summary:
- **Amplitude** = \( |A| \)
- **Period** = \( \frac{2\pi}{|B|} \)

Would you like further details or have any questions?

Here are 5 related questions to expand on this concept:
1. How would the graph change if \( A \) were negative?
2. What is the effect of \( B \) on the frequency of the sine wave?
3. How do you calculate the phase shift in a function like \( y = A \sin(Bx + C) \)?
4. Can you explain how the graph of \( y = \sin(Bx) \) differs from \( y = \cos(Bx) \)?
5. What happens to the graph of \( y = A \sin(Bx) \) if \( A \) becomes larger?

**Tip**: The coefficient \( A \) only affects the vertical scaling (amplitude) but doesn't change the period of the sine wave.

The graph of y = A sin Bx has amplitude = and period =

Explore how to determine the amplitude and period of the trigonometric function y = A sin(Bx). This lesson focuses on using the formulas Amplitude = |A| and Period = 2π / |B| to analyze sine wave graphs, suitable for students in Grades 9-12.

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