詳解：\(y = Si{n^{ - 1}}x\quad  \Rightarrow \quad y' = \frac{{\rm{1}}}{{\sqrt {1 - {x^2}} }}\quad \)，代入點 \(x = \frac{1}{2}\) ，令 \(y' = m\)

\( m = \frac{1}{{\sqrt {1 - {{\left( {\frac{1}{2}} \right)}^2}} }} = \frac{1}{{\sqrt {\frac{3}{4}} }} = \frac{2}{{\sqrt 3 }}\)

利用點斜式，得到切線方程式

\(y - \frac{\pi }{6}\; = \frac{2}{{\sqrt 3 }}(x - \frac{1}{2}\;)\)