9 A curve has equation \(y = \sin ( a x )\), where \(a\) is a positive constant and \(x\) is in radians.
- State the period of \(y = \sin ( a x )\), giving your answer in an exact form in terms of \(a\).
- Given that \(x = \frac { 1 } { 5 } \pi\) and \(x = \frac { 2 } { 5 } \pi\) are the two smallest positive solutions of \(\sin ( a x ) = k\), where \(k\) is a positive constant, find the values of \(a\) and \(k\).
- Given instead that \(\sin ( a x ) = \sqrt { 3 } \cos ( a x )\), find the two smallest positive solutions for \(x\), giving your answers in an exact form in terms of \(a\).
\section*{END OF QUESTION PAPER}