Chapter 6.3, Problem 55E

a.

To determine

To find: the $x\text{-}$ intercepts of the graph. $y=\cos 2x$

Answer to Problem 55E

  $\frac{n\pi }{4}$ (Where n is an odd integer)

Explanation of Solution

Given information:

Consider graph of $y=\cos 2x$ .

Calculation:

The graph of $y=\cos 2x$ is as follows:

  

The x- intercept is the one where the value of y is zero. The graph shows that the x- intercept is at $\frac{n\pi }{4}$ , where n is an odd integer.

b.

To determine

To find: the maximum value of $y$ .

Answer to Problem 55E

1

Explanation of Solution

Given information:

Consider graph of $y=\cos 2x$ .

Calculation:

The graph of $y=\cos 2x$ is as follows:

  

The maximum value of $y$ shown in the graph of $y=\cos 2x$ is 1.

c.

To determine

To find: the minimum value of $y$ .

Answer to Problem 55E

  $-1$

Explanation of Solution

Given information:

Consider graph of $y=\cos 2x$ .

Calculation:

The graph of $y=\cos 2x$ is as follows:

  

The minimum value of $y$ depicted in the graph of $y=\cos 2x$ is $-1$ .

d.

To determine

To find: the period of the function.

Answer to Problem 55E

Explanation of Solution

Given information:

Consider graph of $y=\cos 2x$ .

Calculation:

The graph of $y=\cos 2x$ is as follows:

  

The distance between two adjacent crests or trough is called period. Thus the period for the given function is $\pi$ .

e.

To determine

To sketch: the graph.

Explanation of Solution

Given information:

  $y=\cos 2x$ .

Calculation:

Substitute the value of x in the given function and evaluate y to create a table as shown below.

$x$	$-\pi$	$-\frac{3\pi }{4}$	$-\frac{\pi }{2}$	$-\frac{\pi }{4}$	0	$\frac{\pi }{4}$	$\frac{\pi }{2}$	$\frac{3\pi }{4}$	$\pi$
$y$	1	0	$-1$	0	1	0	$-1$	0	1

Now pair up $x$ and $y$ values to form respective coordinate points. Plot these coordinate points and connect the points to create the graphed function as shown below.