4 It is given that $$x = t + \sin t , \quad y = t ^ { 2 } + 2 \cos t$$ where \(- \pi < t < \pi\). Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(t\). Show that $$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } = \frac { 2 t \sin t } { ( 1 + \cos t ) ^ { 3 } }$$ Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) increases with \(x\) over the given interval of \(t\).