Recall from Calculus that Cartesian coordinates (z,y) ER are related to polar coordinates (r, 0) by...

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Recall from Calculus that Cartesian coordinates (z,y) ER² are related to polar coordinates (r, 0) by T = r cos0, y =r sin 0 where r € (0, ∞) and 9 € [0, 2π]. (a) (By Hand) Write down by hand the expressions for r and in terms of z, y. Show your work. (b) (By MATLAB) Write a script function which takes Cartesian coordinates as input and converts them to their polar counterparts (i.e write the coordinates pair as (r, 0)). (Hint: you could refer Exercise 3 in 03-conditional.pdf, but you need to consider how to make the angles in the interval [0, 2π]) (c) (By MATLAB) Run your function with the following inputs: (x, y) = (-1, 1), (x, y) = (1, -√√3). Recall from Calculus that Cartesian coordinates (z,y) ER² are related to polar coordinates (r, 0) by T = r cos0, y =r sin 0 where r € (0, ∞) and 9 € [0, 2π]. (a) (By Hand) Write down by hand the expressions for r and in terms of z, y. Show your work. (b) (By MATLAB) Write a script function which takes Cartesian coordinates as input and converts them to their polar counterparts (i.e write the coordinates pair as (r, 0)). (Hint: you could refer Exercise 3 in 03-conditional.pdf, but you need to consider how to make the angles in the interval [0, 2π]) (c) (By MATLAB) Run your function with the following inputs: (x, y) = (-1, 1), (x, y) = (1, -√√3).