Chapter 14.8, Problem 25WE

To determine

To find:the solution of the given trigonometric function.

Answer to Problem 25WE

  $\theta ={303.7}^{\circ },{45}^{\circ }$

Explanation of Solution

Given:

The given trigonometric function is $2{\tan }^2\theta +\tan \theta -3=0$ .

Calculation:

As thegiven trigonometric function is $2{\tan }^2\theta +\tan \theta -3=0$ .

Now, to solve the given trigonometric function. Therefore,

  $\begin{array}{l}2{\tan }^2\theta +\tan \theta -3=0\{\text{given equation}}\\ \Rightarrow \left(2\tan \theta +3\right)\left(\tan \theta -1\right)=0\left\{\text{factor}\right\}\\ \therefore 2\tan \theta +1=0\text{ or }\tan \theta -1=0\\ \Rightarrow \tan \theta =\frac{-1}{2}\text{ or }\tan \theta =1\\ \therefore \theta ={303.7}^{\circ }\text{ or }\theta ={45}^{\circ }\end{array}$

Hence, the solution of the given trigonometric function is $\theta ={303.7}^{\circ },{45}^{\circ }$ .