9. (a) Given that \(y = \sin ^ { - 1 } ( \cos \theta )\), where \(0 \leqslant \theta \leqslant \pi\), show that \(\frac { \mathrm { d } y } { \mathrm {~d} \theta } = k\), where the value of \(k\) is to be determined.
(b) Find the value of the gradient of the curve \(y = x ^ { 3 } \tan ^ { - 1 } 4 x\) when \(x = \frac { \pi } { 2 }\).
(c) Find the equation of the normal to the curve \(y = \tanh ^ { - 1 } ( 1 - x )\) when \(x = 1 \cdot 7\).