Chapter 14.5, Problem 4CYU

To determine

To calculate:The value of $\theta$ lying in between $0^{\circ }$ and ${360}^{\circ }$ by the given equation.

Answer to Problem 4CYU

  ${60}^{\circ }and{360}^{\circ }$

Explanation of Solution

Given Information: An Equation $2\cos \theta =1$ is given and $\theta$ lies between $0^{\circ }and{360}^{\circ }$

Formula used: $\cos \theta$ is positive I 1^st and 4^th quadrants.

  $\begin{array}{l}GivenEquationis2\cos \theta =1\\ \therefore \cos \theta =\frac{1}{2}\\ \therefore \cos \theta =\cos {60}^{\circ }or\cos \theta =\cos ({360}^{\circ }-{60}^{\circ })\\ \therefore \theta ={60}^{\circ }or\theta ={300}^{\circ }\end{array}$