Chapter 13, Problem 6CT

To determine

To find: The maximum and minimum values

Answer to Problem 6CT

The maximum and minimum value of $\left[\frac{2\pi }{4}\right]=\left[\frac{\pi }{2}\right]$ .

Explanation of Solution

Given information:

The given function is $y=3\cos 4x$

Calculation:

Consider the graph of the function as shown in the figure (1).

  

Figure (1)

We know that if $y=A\cos \left(Bx-C\right)+D$ is trigonometric function then

Amplitude $=\left[A\right]$

Period $=\left[\frac{2\pi }{B}\right]$

  $\left[\frac{2\pi }{4}\right]=\left[\frac{\pi }{2}\right]$

Therefore the maximum and minimum value of $\left[\frac{2\pi }{4}\right]=\left[\frac{\pi }{2}\right]$