Chapter 13.5, Problem 9CYU

To determine

To calculate: The General solution for $\theta$ by given equation.

Answer to Problem 9CYU

  $n\pi \pm \frac{\pi }{6},n\in z$

Explanation of Solution

Given information: An equation $4{\sin }^2\theta -1=0$ is given

Formula used: ${\sin }^2\theta ={\sin }^2\alpha \Rightarrow \theta =n\pi \pm \alpha ,n\in z.$

Calculation:

  $\begin{array}{l}Givenequationis4{\sin }^2\theta -1=0\\ \Rightarrow 4{\sin }^2\theta =1\\ \Rightarrow {\sin }^2\theta =\frac{1}{4}\\ \Rightarrow {\sin }^2\theta ={\left(\frac{1}{2}\right)}^2\\ \Rightarrow {\sin }^2\theta ={\sin }^2\frac{\pi }{6}\\ \therefore \theta =n\pi \pm \frac{\pi }{6},n\in z\end{array}$