Chapter 9.4, Problem 60E

(a)

To determine

To construct: The table of values for the given function in the interval $-2\pi \le x\le 2\pi$

Answer to Problem 60E

The graph of the model is shown in figure (1) and the water depth is $7\text{ft}$ at time $0\text{and}\text{12}\text{.4}$ .

Explanation of Solution

The values for the function $y=\sin \left(-x\right)$ is tabulated below.

$x$	$y=\sin \left(-x\right)$
$-6.28$	$0$
$-3.14$	$0$
$0$	$0$
$3.14$	$0$
$6.28$	$0$

Table (1)

The values for the function $y=\cos \left(-x\right)$ is tabulated below.

$x$	$y=\cos \left(-x\right)$
$-4.71$	$0$
$-1.57$	$0$
$1.57$	$0$
$4.71$	$0$
$7.85$	$0$

Table (1)

Therefore, the values of the function is tabulated in Table (1) and Table (2).

(b)

To determine

To plot: The graph of each function.

Answer to Problem 60E

The graph of function is shown in figure (1).

Explanation of Solution

Consider the functions.

  $y=\sin \left(-x\right)$

And,

  $y=\cos \left(-x\right)$

The graph of the above function is shown below.

  

Figure (1)

Therefore, the graph of the function is shown in Figure (1).

(c)

To determine

To describe : The transformation of the graph of parent function.

Answer to Problem 60E

The transformation of the graph of parent function is explained below.

Explanation of Solution

Consider the functions.

  $y=\cos \left(-x\right)$

The graph is the vertical of $-1$ units to the graph $y=\cos x$ .

And,

  $y=\sin \left(-x\right)$

The graph is the vertical of $-1$ units to the graph $y=\sin x$ .

Therefore, the transformation of the graph of parent function is explained above.