Chapter 4, Problem 12PS

(a)

To determine

Find one positive value of $x$ less than 5.35 and one value of $x$ greater than 5.35 at which the functions have the same value.

Answer to Problem 12PS

A value of $x$ greater than 5.35 is $7.35$

A value of $x$ smaller than 5.35 is $3.35$

Explanation of Solution

Given:

Two trigonometric functions $f$ and $g$ have periods of $2,$ and their graphs intersect at $x=5.35$

To find a value of $x$ greater than 5.35

  $5.35+2=7.35$

Also, to find a value of $x$ smaller than 5.35

  $5.35-2=3.35$

(b)

To determine

Determine one negative value of $x$ at which the graphs intersect.

Answer to Problem 12PS

One negative value of $x$ at which the graphs intersect $-0.65$

Explanation of Solution

Given:

Two trigonometric functions $f$ and $g$ have periods of $2,$ and their graphs intersect at $x=5.35$

To find a negative value of $x$

  $5.35-3(2)=-0.65$ .

(c)

To determine

Determine whether it is true or false.

Answer to Problem 12PS

The given statement is true

Explanation of Solution

Given:

Two trigonometric functions $f$ and $g$ have periods of $2,$ and their graphs intersect at $x=5.35$

  $f(13.35)=g(-4.65)$

Yes, the given statement is true.

There is a difference of nine periods between the values.