A curve has equation \(y=5\cos3x-2\sin ax\), where \(a\) is a positive constant.
Find, in terms of \(a\), the equations of the tangent and normal to the curve at the point \(R\) where \(x=0\).[6]
The tangent cuts the \(x\)-axis at the point \(S\) and the normal cuts the \(y\)-axis at the point \(T\). Given that length \(ST\) is 6 units, find the value of \(a\).[4]