The amplitude of a sinusoidal function of the form \( y = a \sin x \) or \( y = a \cos x \) is determined by the absolute value of the coefficient \( a \).

In the given function \( y = -8 \sin x \), the coefficient \( a \) is \(-8\).

Thus, the amplitude is the absolute value of \(-8\), which is:

\[
\text{Amplitude} = |-8| = 8
\]

The amplitude of \( y = -8 \sin x \) is 8.

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Do you want further details or have any questions about sinusoidal functions? Here are some related questions you might find interesting:

1. What is the period of the function \( y = -8 \sin x \)?
2. How does the negative sign in front of the amplitude affect the graph of \( y = -8 \sin x \)?
3. What is the phase shift of the function \( y = -8 \sin(x - \frac{\pi}{4}) \)?
4. How does the amplitude affect the graph of a sine function?
5. What is the vertical shift of the function \( y = -8 \sin x + 3 \)?
6. How would the function \( y = -8 \sin x \) look if the amplitude were 4 instead?
7. How does the amplitude compare between \( y = -8 \sin x \) and \( y = 8 \sin x \)?
8. Can you explain how to graph the function \( y = -8 \sin x \)?

**Tip:** When analyzing trigonometric functions, always start by identifying the amplitude, period, phase shift, and vertical shift to understand their graphical behavior.

Explore the amplitude of the sinusoidal function y = -8 sin x with a clear explanation and calculation. This problem delves into trigonometric concepts and the calculation of function amplitudes. Suitable for high school students in Grades 10-12.

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