<s>[INST] Equations with Sinus. How to find equation solution? I don't understand how to get a solution for sinus equation.
I have:
$$\sin x = \frac{1}{2}$$
\begin{align*}
x & = (-1)^k \cdot \arcsin\left(\frac{1}{2}\right) + 180^\circ \cdot k, k \in \mathbb{Z}\\
  & = (-1)^k \cdot 30^\circ + 180^\circ \cdot k, k \in \mathbb{Z}
\end{align*}
Answer: $x = \ldots$
How to find x? 
 [/INST] what you have $x = (-1)^k 30^\circ+180^\circ \cdot k$  is correct.
but can also be done the following way.
the solutions of $$\sin x = \frac 12$$  are $$x = \sin^{-1}(1/2) + k\cdot 360^\circ, 180 - \sin^{-1}(1/2) + k\cdot 360^\circ \\
x = 30^\circ + k\cdot 360^\circ, 150^\circ + k\cdot 360^\circ, \quad k \text{ any integer.} $$
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