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.