$2\mathrm{.}13$ A two$-$dimensional vector in a Cartesian plane can be represented in either rect$-$

angular coordinates $(x,y)$ or the polar coordinates $(r,),$ as shown in Figure $2\mathrm{.}22.$

The relationships among these two sets of coordinates are given by the following

equations:

$x=rcos$

$y=rsin$

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

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

Use the MATLAB help system to look up function atan$2,$ and use that func$-$

tion in answering the following questions.

$($a$)$ Write a program that accepts a two$-$dimensional vector in rectangular coor$-$

dinates and calculates the vector in polar coordinates, with the angle $$

expressed in degrees.

$($b$)$ Write a program that accepts a two$-$dimensional vector in polar coordinates

$($with the angle in degrees$)$ and calculates the vector in rectangular coordinates.