Chapter 7.4, Problem 15E

To determine

To find: The solution of the equation $\tan \theta =5$ .

Answer to Problem 15E

The solution of the equation $\tan \theta =5$ is $\theta =1.374+k\pi$ .

Explanation of Solution

Given information:

The given equation is $\tan \theta =5$ .

Calculation:

As tangent has period $\pi$ , So first find the solutions in $\left(-\frac{\pi }{2},\frac{\pi }{2}\right)$ .

As the given equation is $\tan \theta =5$ .

Therefore, the solution to the equation in $\left(-\frac{\pi }{2},\frac{\pi }{2}\right)$ are

  $\begin{array}{c}\theta ={\tan }^{-1}\left(5\right)\\ =1.374\end{array}$

As tangent repeats its values after every $\pi$ units.

So, the general solution of the equation is given by

  $\theta =1.374+k\pi$ .

Therefore, the solution of the equation $\tan \theta =5$ is $\theta =1.374+k\pi$ .