Question

How do you solve `sin(x)=1/2`?

Answer 1

The solutions are:

`x=pi/6+2kpi`

and

`x=5/6pi+2kpi`.

Draw the trigonometric circle and a line passing from `O` with a slope of `alpha=pi/6`. That line intercept the circle in a point `A`, make the perpendicular from that point to the x-axis, the interception is `B`.
The triangle `OAB` is half of an equilater triangle with `OA=1` and `AB=1/2`. So `sinalpha=(AB)/(OA)=1/2`.

You can say the same with the other line with `alpha=5/6pi`.