Answer:
2
Step-by-step explanation:
Consider two functions:
[tex]y=\sin x[/tex] and [tex]y=\sin 2x[/tex]
The period of each function is
[tex]2\pi[/tex] and [tex]\pi[/tex]
This means that the graph of the function [tex]y=\sin x[/tex] (red graph) intersects by the horizontal line [tex]y=\frac{1}{2}[/tex] twice and the graph of the function [tex]y=\sin 2x[/tex] intersects by the horizontal line [tex]y=\frac{1}{2}[/tex] four times (blue graph) for [tex]x\in [0,2\pi ).[/tex]
So the equation [tex]\sin \theta=\dfrac{1}{2}[/tex] has 2 solutions and the equation [tex]\sin 2\theta=\dfrac{1}{2}[/tex] has 4 solutions. Thus, the difference is 2.
