Chapter 14.8, Problem 5WE

To determine

To find:the solution of the given trigonometric function.

Answer to Problem 5WE

  $x=\frac{3\pi }{4}$

Explanation of Solution

Given:

The given trigonometric function is $\sin \theta +\cos \theta =0$ .

Calculation:

As thegiven trigonometric function is $\sin \theta +\cos \theta =0$ .

Now, to solve the given trigonometric function. Therefore,

  $\begin{array}{l}\sin \theta +\cos \theta =0\{\text{given equation}}\\ \therefore \sin \theta =-\cos \theta \{\text{subtract both sides by }\cos \theta \text{}}\\ \frac{\sin \theta }{\cos \theta }=-\frac{\cos \theta }{\cos \theta }\{\text{divide both sides by }\cos \theta \text{}}\\ \tan \theta =-1\\ \tan \theta =-\tan \frac{\pi }{4}\left\{\because \tan \frac{\pi }{4}=1\right\}\\ x=-\frac{\pi }{4}\\ \{\because tan\theta \text{ lies in quadrant III}\}\\ \therefore x=\pi +\left(-\frac{\pi }{4}\right)=\frac{3\pi }{4}\end{array}$

Hence, the solution of the given trigonometric function is $x=\frac{3\pi }{4}$ .