Chapter 4.6, Problem 49E

To determine

To find: the solutions of the equation in the interval $\left[-2\pi ,2\pi \right]$ .

Answer to Problem 49E

  $x=-\left(\frac{7\pi }{4}\right),-\left(\frac{3\pi }{4}\right),\left(\frac{\pi }{4}\right)$ and $\left(\frac{5\pi }{4}\right)$ .

Explanation of Solution

Given information:

Given function is

  $y=\tan x=1$ .

Calculation:

Let us consider the points to solve the equation $\tan x=1$ .

Let us, first plot the graph for $f\left(x\right)=\tan x$

Now, in the above graph, look for all the points on the graph where the value of $\tan x$ is 1.

From the above graph, it can be een that the value of $\tan x$ equal to 1 at

  $x=-\left(\frac{7\pi }{4}\right),-\left(\frac{3\pi }{4}\right),\left(\frac{\pi }{4}\right)$ and $\left(\frac{5\pi }{4}\right)$

Therefore,

  $x=-\left(\frac{7\pi }{4}\right),-\left(\frac{3\pi }{4}\right),\left(\frac{\pi }{4}\right)$ and $\left(\frac{5\pi }{4}\right)$ .