6. A curve has parametric equations
$$x = \tan ^ { 2 } t , \quad y = \sin t , \quad 0 < t < \frac { \pi } { 2 }$$
- Find an expression for \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(t\). You need not simplify your answer.
- Find an equation of the tangent to the curve at the point where \(t = \frac { \pi } { 4 }\).
Give your answer in the form \(y = a x + b\), where \(a\) and \(b\) are constants to be determined.
- Find a cartesian equation of the curve in the form \(y ^ { 2 } = \mathrm { f } ( x )\).
\section*{LU}