Chapter 13.5, Problem 5CYU

To determine

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

Answer to Problem 5CYU

  $\theta ={210}^{\circ }or{150}^{\circ }$

Explanation of Solution

Given Information: An Equation $\cos \theta =\frac{\sqrt{3}}{2}$ is given.

Formula used: $\cos \theta$ is Negative in 2^nd and 3^rd quadrants. $\cos (\pi \pm \theta )=-\cos \theta$

Calculation:

  $\begin{array}{l}GivenEquationis\\ \cos \theta =\frac{\sqrt{3}}{2}\\ \therefore \cos \theta =-\cos {30}^{\circ }\\ \therefore \cos \theta =\cos ({180}^{\circ }-{30}^{\circ })or\cos ({180}^{\circ }-{30}^{\circ })\\ \therefore \theta ={150}^{\circ }or{210}^{\circ }\end{array}$