Problem $3\mathrm{.}4$ Call the function FirstName$\_$LastName$\_$CartToPolar.m$.$

Test your program in the command window evaluating the following cases:

$\backslash$table$[[$x$,$Y$,$r$,\backslash$theta $],[2,0,,],[2,1,,],[0,3,,],[-3,1,,],[-2,0,,],[-1,-2,,],[0,0,,],[0,-2,,],[2,3,,]]$

Two distances are required to specify the location of a point relative to an origin in two$-$

dimensional space:

The horizontal and vertical distances $(x,y)$ in Cartesian coordinates.

The radius and angle $(r,$ in polar coordinates.

It is relatively straightforward to compute Cartesian coordinates $(x,y)$ on the basis of polar

coordinates $(r,).$ The reverse process is not so simple. The radius can be computed by the

following formula:

$r=\sqrt[\phantom{2}]{x^2+y^2}$

If the coordinates lie within the first and fourth coordinates $($i$.$e$.,x>0),$ then a simple formula

can be used to compute $$ :

$=ta{n}^{-1}(\frac{y}{x})$

The difficulty arises for the other cases. The following table summarizes the possibilities: