Bentuk Dasar

\begin{equation*}
\begin{split}
& \sin 2x  = 0,5 \\\\
& \sin 2x  = \sin \frac{1}{6} \pi
\end{split}
\end{equation*}

Solusi 1

\begin{equation*}
\begin{split}
2x &  = \frac{1}{6} \pi + k \:.\: 2 \pi \\\\
x &  = \frac{1}{12} \pi +  k \:.\: \pi \\\\
k & = 0 \rightarrow {\color {red} x = \frac{1}{12} \pi} \\\\
k & = 1 \rightarrow {\color {red} x = 1\frac{1}{12} \pi}
\end{split}
\end{equation*}

Solusi 2

\begin{equation*}
\begin{split}
2x &  = \left(\pi - \frac{1}{6} \pi \right) + k \:.\: 2 \pi  \\\\
2x &  = \frac{5}{6} \pi + k \:.\: 2 \pi \\\\
x &  = \frac{5}{12} \pi + k \:.\: \pi \\\\
k & = 0 \rightarrow {\color {red} x = \frac{5}{12} \pi} \\\\
k & = 1 \rightarrow {\color {red} x = 1\frac{5}{12} \pi}
\end{split}
\end{equation*}

HP = \(\left\{\frac{1}{12} \pi, \frac{5}{12} \pi, 1\frac{1}{12} \pi, 1\frac{5}{12} \pi\right\}\)