Question

In Exercises \(17-22,\) specify (a) the period, (b) the amplitude, and (c) identify the viewing window that is shown. $$y=2 \cos 3 x$$

Short answer

The amplitude of the function \(y = 2 \cos 3x\) is 2, the period is \(2\pi/3\), and the viewing window should ideally include x-values that are multiples of \(2\pi/3\) and y-values that range from -2 to 2.

Step-by-step solution

Find the Amplitude

The amplitude of the function is given by the absolute value of the coefficient of the cosine function. Here the coefficient of the cosine function is 2, so the amplitude is |2| = 2.

Find the Period

The period of a cosine function is given by \(2\pi/k\), where \(k\) is the coefficient of \(x\). Here the coefficient of \(x\) is 3, so the period is \(2\pi/3\).

Identify the Viewing Window

The viewing window of the function includes the maxima, minima and points of inflection. Since the amplitude is 2 and the period is \(2\pi/3\), the maxima, minima will lie between -2 and 2 and the x-value for these points will be multiples of the period \(2\pi/3\).