Chapter 14.8, Problem 11WE

To determine

To find:the solution of the given trigonometric function.

Answer to Problem 11WE

  $\theta =-{25}^{\circ }$

Explanation of Solution

Given:

The given trigonometric function is $\sin \left(\theta +{25}^{\circ }\right)=0$ .

Calculation:

As thegiven trigonometric function is $\sin \left(\theta +{25}^{\circ }\right)=0$ .

Now, to find the value of the given trigonometric function. Therefore,

  $\begin{array}{l}\sin \left(\theta +{25}^{\circ }\right)=0\{\text{given equation}}\\ \therefore \left(\theta +{25}^{\circ }\right)={\sin }^{-1}0\\ \left(\theta +{25}^{\circ }\right)={\sin }^{-1}\left(\sin 0\right)\left\{\because \sin 0=0\right\}\\ \left(\theta +{25}^{\circ }\right)=0^{\circ }\left\{{\sin }^{-1}\left(\sin x\right)=x\right\}\\ \therefore \theta =0-{25}^{\circ }\left\{\text{subtract }{25}^{\circ }\text{ on both sides}\right\}\\ \theta =-{25}^{\circ }\end{array}$

Hence, the solution of the given trigonometric function is $\theta =-{25}^{\circ }$ .