Maths Question:
$\begin{align} & \text{Write down the general solution of the trigonometric equations} \\ & 2\sin 2\theta +1=0 \\\end{align}$
Maths Solution:
$\begin{align} & 2\sin 2\theta +1=0 \\ & 2\sin 2\theta =-1 \\ & \sin 2\theta =-\frac{1}{2} \\ & 2\theta ={{\sin }^{-1}}\frac{1}{2} \\ & 2\theta ={{30}^{\circ }} \\ & \text{The general solution is } \\ & 2\theta =n{{180}^{\circ }}+{{(-1)}^{n}}({{30}^{\circ }}) \\ & \theta =\frac{n{{180}^{\circ }}+{{(-1)}^{n}}({{30}^{\circ }})}{2}=n{{90}^{\circ }}+{{(-1)}^{n}}({{30}^{\circ }}) \\\end{align}$
University mathstopic: