Chapter 4.6, Problem 84E

To determine

Distance $d$ .

Graph the function over the interval $-\pi /2<x<\pi /2$

Answer to Problem 84E

  

Explanation of Solution

Given information:

A television camera is on a reviewing platform 27 meters from the street on which a parade will be passing from left to right (see figure). Write the distance $d$ from the camera to a particular unit in the parade as a function of the angle $x$ and graph the function over the interval $-\pi /2<x<\pi /2$ .Consider as negative $x$ when a unit in the parade approaches from the left.)

Calculation:

Let us consider the points to write $d$ as a function of angle .

Let $A$ be the point where camera is situated.

  $B$ is the point on the street where the parade will be passing left to right.

  $C$ is the point where particular unit of parade will reach.

So here, the points form a right angled triangle(right angled at $B$ )

In triangle $ABC$ ,

Distance of the camera from the particular unit in the parade( $AC$ )= $d$

Distance of the camera from the street on which parade will pass( $AB$ )= $27m.$

Angle between $AB$ and $AC$ = $x$

Now using,

  $\cos x=\begin{array}{c}AB\\ AC\end{array}$

  $\cos x=\begin{array}{c}27\\ d\end{array}$

  $d=\begin{array}{c}27\\ \cos x\end{array}$

Now, let us plot $d=\begin{array}{c}27\\ \cos x\end{array}$ over the interval $-\pi /2<x<\pi /2$ ,

  

Hence the above graph represents the $d$ as a function of $x$ over the interval $-\pi /2<x<\pi /2$ .