# Bentuk Mengubah Fungsi

### Bentuk Mengubah Fungsi

Beberapa soal limit trigonometri dapat diselesaikan dengan mengubah fungsi trigonometri, seperti beberapa contoh berikut:

Contoh 01

\begin{equation*}
\begin{split}
& \lim_{x \rightarrow \: \pi} \: \frac{\sin x}{\pi-x} \\\\
& \lim_{x \rightarrow \: \pi} \: \frac{\sin (\pi - x)}{\pi-x} \\\\
& \lim_{x \rightarrow \: \pi} \: \frac{\cancel{\sin (\pi - x)}}{\cancel{\pi-x}} \\\\
& \bbox[5px, border: 2px solid magenta] {1}
\end{split}
\end{equation*}

Contoh 02

\begin{equation*}
\begin{split}
& \lim_{x \rightarrow \: \frac 12 \pi} \: \frac {\cos x}{x - \frac 12 \pi} \\\\
& \lim_{x \rightarrow \: \frac 12 \pi} \: \frac {\sin (\frac 12 \pi - x)}{-(\frac 12 \pi - x)} \\\\
& \lim_{x \rightarrow \: \frac 12 \pi} \: \frac {\cancel{\sin (\frac 12 \pi - x)}}{- \cancel{(\frac 12 \pi - x)}} \\\\
& \bbox[5px, border: 2px solid magenta] {- 1}
\end{split}
\end{equation*}

Contoh 03

\begin{equation*}
\begin{split}
& \lim_{x \rightarrow \: 1} \: (x-1) \:.\: \cot \pi x \\\\
& \lim_{x \rightarrow \: 1} \: \frac {x - 1}{\tan \pi x} \\\\
& \lim_{x \rightarrow \: 1} \: \frac {x - 1}{-\tan (\pi - \pi x)} \\\\
& \lim_{x \rightarrow \: 1} \: \frac {x - 1}{-\tan \pi(1 - x)} \\\\
& \lim_{x \rightarrow \: 1} \: \frac {\cancel{x - 1}}{- \cancel{\tan \pi (1 - x)}} \\\\
& \bbox[5px, border: 2px solid magenta] {- \frac {1}{\pi}}
\end{split}
\end{equation*}