Solve each equation for all θ in radians
sin θ = 1
answer: π/2 +2Nπ
π=Pie
For $\displaystyle \sin \theta = 1 $ there are an infinite number of solutions since the sine wave is continuous and is no restriction is set in the question. To find first you simply take the arcsin of 1:
$\displaystyle \theta = \arcsin 1 $
$\displaystyle \theta = 1.57... $
which is equivalent to $\displaystyle \frac {\Pi}{2} $
The above answer is the only time the sine wave has a y value of 1 for $\displaystyle 0 \leq \theta \leq 2\Pi$. However the question asks for all values of $\displaystyle \theta $. For the rest of the solutions you add $\displaystyle \frac 2\Pi n $
Where n is any integer negative or positive. The 2$\displaystyle \Pi$ is used as the wave repeats every $\displaystyle 2\Pi $ and the n covers the fact that is repeats n times in a positive and negative direction.
Hope this helps you to understand it. If you need further explanation just ask.
you are expected to know that if $\displaystyle \sin{\theta} = 1$, then the primary value of $\displaystyle \theta = \frac{\pi}{2}$ , and repeats for values of $\displaystyle \frac{\pi}{2} + k \cdot 2\pi \, \, , \, \, k \in \mathbb{Z}$.
learn the unit circle ...
btw, this is pi ...
and this is pie ...