Chapter 4.5, Problem 63E

Solution

To calculate : The distance of $d$ from the camera to a particular parade float as function of angle $x$ and graph the function over the interval $-\frac{\pi }{2}<x<\frac{\pi }{2}$ if a television camera is on platform 30 m from the point on high street.

  

The value of $\cot x$ as a reflection about the $x$ -axis of a horizontal translation of $\tan x$ is $\cot x=-\tan \left(x-\frac{\pi }{2}\right)$ .

Given information:

A television camera is on platform 30 m from the point on high street.

  

Formula:

Use the right-angle property of trigonometric angles to calculate the distance.

Calculation:

Consider the following figure,

  

Express the distance $d$ as the function of the angle $x$ by letting $\theta =x$ , $adj=30$ and $hyp=d$ .

  $\cos x=\frac{30}{d}$

  $\begin{array}{c}d=\frac{30}{\cos x}\\ d=30\sec x\end{array}$

The graph of the function over the interval $-\frac{\pi }{2}<x<\frac{\pi }{2}$ .

  

Thus, the distance of $d$ from the camera to a particular parade float as function of angle $x$ is $d=30\sec x$ .