Chapter 4, Problem 12PS

To determine

To solve: To provide the positive value of $x$ which is greater than $5.35$ and less than $5.35$ .

Answer to Problem 12PS

One positive value of $x$ which is greater than $5.35$ is $5.5$ and one positive value which is less than $5.35$ is $5$ at which value of function is same.

Explanation of Solution

Given information:

Two trigonometric functions $f$ and $g$ have periods of $2$ and their graphs intersects somewhere at point $x$ .

Graph:

The graph of the statement is mentioned below.

  

The graph above mentioned is on real number line on the x axis and y axis.

The graph mentioned above is $f\left(x\right)=\sin \pi x$ and $g\left(x\right)=\cos \pi x$ .

Here as we observed in the above mentioned graph that the function is $f\left(x\right)=\sin \pi x$ and $g\left(x\right)=\cos \pi x$ .Since as in the mentioned problem the function has period 2.

Since we know that period of $\sin x$ and $\cos x$ is $2\pi$ .

Therefore we assume the function which has period 2 is $f\left(x\right)=\sin \pi x$ and $g\left(x\right)=\cos \pi x$ .

Therefore the curve is periodic.

The value of $x$ just greater than $5.35$ is $5.5$ and the value of $x$ just less than $5.35$ is $5$ where $f\left(x\right)=\sin \pi x$ at $x=5.5$ is $\sin \left(\pi *5.5\right)=-1$ and $g\left(x\right)=\cos \pi x$ at $x=5$ is $\cos \left(\pi *5\right)=-1$

  $-1$ .

Therefore one positive value of $x$ is $5.5$ and another value is $5$ for which the value of function is same.