Chapter SH, Problem 13.20EP

To determine

To find:

The each expression into trigonometric form

Answer to Problem 13.20EP

The exact value is $\theta ={120}^0,{30}^0$

Explanation of Solution

Given:

  ${\text{4cos}}^2\theta -\text{1=}\text{0}$

Concept used:

Trigonometric ratios: - Atrigonometric ratio are the ratios between edges of a right triangle.

Calculation:

Trigonometric ratio is

  $\begin{array}{l}{\text{4cos}}^2\theta -\text{1=}\text{0}\\ 4{\cos }^2\theta =1\\ {\cos }^2\theta =-\frac{\text{1}}{4}\\ \cos \theta =\pm \frac{\text{1}}{2}\\ \theta =\frac{2\pi }{3},\frac{\pi }{3}\\ \theta ={120}^0,{30}^0\end{array}$