$1-19($modified$)$ For the two$-$link manipulator in the figure below, suppose both link lengths are $1.$

Find the coordinates of tool when ${}_1=\frac{}{6}$rad and ${}_2=\frac{}{2}$rad.

If the joint velocities are constant at ${}_1^{}=1\frac{\text{r}\text{a}\text{d}}{sec}$ and ${}_2^{}=2\frac{\text{r}\text{a}\text{d}}{sec},$ what is the translational velocity of the tool as a function of ${}_1$ and ${}_2?$ What is the instantaneous tool velocity when ${}_1={}_2=\frac{}{4}$rad?

Generate a MATLAB simulation to that uses your solutions in $(2)$ to create an x$-$y plot of the tool position as a function of time in Cartesian coordinates. Assume the robot starts at ${}_1={}_2=0$rad and the simulation runs for $2$ seconds with a step size of $0\mathrm{.}1$ seconds per step.