Problem

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.)

Solution

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 \(\boxed{\frac{2\pi}{5}}\).

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Source: https://solvelyapp.com/problems/foauaGIL29/

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