Determine the amplitude and period of the following function without graphing.
\[
y=-3 \cos (5 x)
\]
The amplitude is $\square$.
The period is $\square$.
(Simplify your answer. Type an exact answer in terms of $\pi$. Use integers or fractions for any numbers in the expression.)
Answer
The period of a cosine function is \(\frac{2\pi}{|b|}\), where \(b\) is the coefficient of \(x\). So, the period of the given function is \(\frac{2\pi}{|5|}\), which simplifies to \(\boxed{\frac{2\pi}{5}}\).
Step 1 ：The given function is \(y=-3 \cos (5 x)\).
Step 2 ：The amplitude of a cosine function is the absolute value of the coefficient of the cosine term. So, the amplitude of the given function is \(|-3|\), which simplifies to \(\boxed{3}\).
Step 3 ：The period of a cosine function is \(\frac{2\pi}{|b|}\), where \(b\) is the coefficient of \(x\). So, the period of the given function is \(\frac{2\pi}{|5|}\), which simplifies to \(\boxed{\frac{2\pi}{5}}\).
