hi evreyone,
here is the q:
Find the solutions of the equation sin θ = 1/2 if:
(a) θ is in the interval [0, 2 pi )
(b) θ is any real number
If $\displaystyle \theta$ is a solution of $\displaystyle \sin(\theta)=1/2$ then so is $\displaystyle \theta_n = \theta+2\pi n, \ \ n=\pm 1, \ \pm 2, ...$.
So using the solutions given by ImPerfectHacker we have:
$\displaystyle \pi/6+2 \pi n, n=0,\ \pm 1,\ \pm 2,\ ...$, and $\displaystyle 5 \pi/6+2 \pi n, n=0,\ \pm 1,\ \pm 2,\ ...$ comprise all the real solution.
RonL