The point \(\mathrm { P } ( 4 , - 2 )\) lies on the curve \(y = \mathrm { f } ( x )\). Find the coordinates of the image of P when the curve is transformed to \(y = \mathrm { f } ( 5 x )\).
Describe fully a single transformation which maps the curve \(y = \sin x ^ { \circ }\) onto the curve \(y = \sin ( x - 90 ) ^ { \circ }\).