$(7$ marks in total$)$

The robot arm in Figure $7$ is moved such that the position of grip $A$ is given by

$r=2cos,z=sin(4)$

where $$ is a function of time $t,$ and is twice differentiable. That is$,{}^{}$ and ${}^{}$ both exist and are nonzero in general. Write the following expressions in terms of ${}^{}$ and ${}^{}$

$r^{}(1$ mark$)$

$r^{}(2$ marks$)$

$z^{}(1\mathrm{.}5$ marks$)$ and

$z^{}(2\mathrm{.}5$ marks$)$