Graph the following function over a two-period interval. Give the period and the amplitude.
$$y=-3\cos 5x$$
What is the period of the function $y=-3\cos 5x$ ?
(Simplify your answer. Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.)
What is the amplitude of the function $y=-3\cos 5x$ ?
(Type an integer or a simplified fraction.)
Which of the following is the correct graph of the function $y=-3\cos 5x$ ?
A.
B.
C.
D.

Step 1 ：First, we need to find the period of the function. The period of a function of the form $y=a\cos (bx)$ or $y=a\sin (bx)$ is given by $\frac{2\pi }{|b|}$.

Step 2 ：In this case, $b=5$, so the period of the function $y=-3\cos 5x$ is $\frac{2\pi }{5}$.

Step 3 ：Next, we need to find the amplitude of the function. The amplitude of a function of the form $y=a\cos (bx)$ or $y=a\sin (bx)$ is given by $|a|$.

Step 4 ：In this case, $a=-3$, so the amplitude of the function $y=-3\cos 5x$ is $3$.

Step 5 ：Finally, we need to graph the function over a two-period interval. The function $y=-3\cos 5x$ is a cosine function with a period of $\frac{2\pi }{5}$ and an amplitude of 3, and it is reflected about the x-axis because the coefficient of the cosine function is negative.

Step 6 ：The graph of the function $y=-3\cos 5x$ over a two-period interval is shown below:

Step 7 ：$$\text{Graph of }y=-3\cos 5x$$

Step 8 ：$$\text{The period of the function }y=-3\cos 5x\text{ is }\boxed{{\displaystyle \frac{2\pi }{5}}}.$$

Step 9 ：$$\text{The amplitude of the function }y=-3\cos 5x\text{ is }\boxed{{\displaystyle 3}}.$$