Suppose a path is traced by the parametric equations $\backslash ($ x$=3-\backslash$cos $^\{2\}$ t $\backslash )$ and $\backslash ($ y$=\backslash$cos t $\backslash ).$

a$.$ Sketch the graph. Include the direction and label at least two points.

b$.$ Eliminate the parameter to get the function as a simple $\backslash ($ y $\backslash )$ in terms of $\backslash ($ x $\backslash ),$ noting any restrictions.

c$.$ Find $\backslash (\backslash$frac$\{$d y$\}\{$d x$\}\backslash )$ using the parametric formula. Show that this is equal to the derivative of the function you get in part b using standard derivatives.

d$.$ Find the area under the curve $($to the y$-$axis$)$ using the parametric equations. Explain how you chose the limits of integration.