Tentukan nilai x yang memenuhi persamaan:
\(\sin 2x = \cos x\) dimana \(0^{\text{o}} \leq x \leq 360^{\text{o}}\)
\begin{equation*}
\begin{split}
& \sin 2x = \cos x \\\\
& \sin 2x = \sin (90 - x)^{\text{o}}
\end{split}
\end{equation*}
Solusi 1
\begin{equation*} \begin{split} 2x & = 90^{\text{o}} - x + k \:.\: 360^{\text{o}} \\\\ 3x & = 90^{\text{o}} + k \:.\: 360^{\text{o}} \\\\ x & = 30^{\text{o}} + k \:.\: 120^{\text{o}} \\\\ k & = 0 \rightarrow {\color {red} x = 120^{\text{o}}} \\\\ k & = 1 \rightarrow {\color {red} x = 150^{\text{o}}} \\\\ k & = 2 \rightarrow {\color {red} x = 270^{\text{o}}} \end{split} \end{equation*}
Solusi 2
\begin{equation*} \begin{split} 2x & = (180 - (90 - x))^{\text{o}} + k \:.\: 360^{\text{o}} \\\\ 2x & = 90^{\text{o}} + x + k \:.\: 360^{\text{o}} \\\\ x & = 90^{\text{o}} + k \:.\: 360^{\text{o}} \\\\ k & = 0 \rightarrow {\color {red} x = 90^{\text{o}}} \end{split} \end{equation*}
HP = \(\{90^{\text{o}}, 120^{\text{o}}, 150^{\text{o}}, 270^{\text{o}} \}\)