Chapter 14.8, Problem 14OE

To determine

To outline:a strategy for solving the given equation.

Answer to Problem 14OE

  $\theta ={85}^{\circ }$ .

Explanation of Solution

Given:

The given equation is $2\cos \left(\theta -{25}^{\circ }\right)=1$ .

Calculation:

As thegiven equation is $2\cos \left(\theta -{25}^{\circ }\right)=1$ .

Now, to find the solutions of the given equation. Therefore,

  $\begin{array}{l}2\cos \left(\theta -{25}^{\circ }\right)=1\{\text{given equation}}\\ \cos \left(\theta -{25}^{\circ }\right)=\frac{1}{2}\{\text{divide both sides by }2\text{}}\\ \Rightarrow \cos \left(\theta -{25}^{\circ }\right)=\cos {60}^{\circ }\left\{\cos {60}^{\circ }=\frac{1}{2}\right\}\\ \therefore \left(\theta -{25}^{\circ }\right)={60}^{\circ }\\ \theta ={60}^{\circ }+{25}^{\circ }\left\{{\text{add both sides by 25}}^{\circ }\right\}\\ \theta ={85}^{\circ }\end{array}$

Hence, the solutions of the given equation is $\theta ={85}^{\circ }$ .