Chapter 6.1, Problem 66E

To determine

To find : The value of $g(x)$

Answer to Problem 66E

The answer is: $g(x)=-\cos x$

Explanation of Solution

Given information:

The differential equations $dy/dx=\sec x$

And $dy/dx=g(x)$ are perpendicular.

Calculation:

If $\sec x$ and $g(x)$ are perpendicular, then $g(x)$ must be the negative reciprocal of $\sec x$ .

  $\begin{array}{c}g(x)=-\frac{1}{\sec x}\\ \Rightarrow g(x)=-\cos x\end{array}$

Therefore, the required value of $g(x)=-\cos x$ .