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To solve for the period and amplitude of the function \( y = -\sin(4x) \), let's break it down:

### 1. Amplitude:
For a sine function in the form \( y = A \sin(Bx) \), the amplitude is given by the absolute value of \( A \). In this case, the equation is \( y = -\sin(4x) \), which means \( A = -1 \). The amplitude is the absolute value of \( A \), so:
\[
\text{Amplitude} = |A| = |-1| = 1
\]

### 2. Period:
The period of a sine function is determined by the coefficient \( B \) inside the argument of the sine. The formula for the period of \( \sin(Bx) \) is:
\[
\text{Period} = \frac{2\pi}{|B|}
\]
In this case, \( B = 4 \), so the period is:
\[
\text{Period} = \frac{2\pi}{4} = \frac{\pi}{2}
\]

### Final Answer:
- **Period**: \( \frac{\pi}{2} \)
- **Amplitude**: 1

Would you like further details or have any questions?

Here are some related questions:
1. How does the negative sign in the function affect the graph?
2. What is the general form of a sine function and how does it relate to phase shift?
3. How would the period change if the coefficient of \( x \) were different?
4. How do you calculate the frequency of a sine wave based on its period?
5. How does the amplitude affect the range of a sine function?

**Tip**: The period of a sine or cosine function is always affected by the coefficient inside the argument. The larger the coefficient, the smaller the period.

Find the period and amplitude of the function y = -sin(4x).

Learn how to calculate the period and amplitude of the trigonometric function y = -sin(4x). The amplitude is 1, and the period is π/2, based on the formula 2π / B. This problem is suitable for students in Grades 9-12.

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