Chapter 4.5, Problem 89E

To determine

To find the statement is true or false.

Answer to Problem 89E

So, False the graph of the function given by $g(x)=\sin (x+2\pi )$ translates the

graph of $f(x)=\sin x$ one period to the left because C is negative.

Explanation of Solution

Given information: The graph of the function given by $g(x)=\sin (x+2\pi )$ translates the

graph of $f(x)=\sin x$ one period to the right.

Calculation:

The graph of the function given by $g(x)=\sin (x+2\pi )$ translates the

graph of $f(x)=\sin x$ one period to the right. Then the equation for a sine is,

  $y=A\sin (B(x-C))+D$ .

If C is negative, the graph would be shifted to the left. If C is positive, the graph would be shifted to the right.

In this case the equation of g(x) is,

  $y=1\sin (1(x-(-C)))+0$ .

The product of two negatives results in a positive which is why it seems like C is positive when accurately, it is negative.

So, False the graph of the function given by $g(x)=\sin (x+2\pi )$ translates the

graph of $f(x)=\sin x$ one period to the left because C is negative.