Answer:
The values of x are:
[tex]x=\frac{\pi }{12},\:x=\frac{5\pi }{12}\\[/tex]
Step-by-step explanation:
To solve the trigonometric equations, we need to know the general solution of each trigonometric ratios involved in the equation and also need to know the inverse trigonometric ratio values.
Now, here the trigonometric equation is:
[tex]\sin \left(2x\right)=\frac{1}{2},\:0\le \:x<2[/tex]
So the general solution will be given by:
[tex]\sin \left(2x\right)=\frac{1}{2}\\\Rightarrow 2x=\frac{\pi }{6},\:2x=\frac{5\pi }{6}\\\Rightarrow x=\frac{\pi }{12},\:x=\frac{5\pi }{12}[/tex]
So we will have two values of x in the given restricted domain.
