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Math Help - is it possible to convert equation variable (polar to Cartesian coordinate)?

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    is it possible to convert equation variable (polar to Cartesian coordinate)?

    hi everyone!!
    my project is related spur gear and i draw the involute profile by using matlab program .
    this is the program only for better understanding (graph also attached with post)
    is it possible to make such kind of equation Y=f(x) for involute profile?
    because i want to use this equation in bending, deflection, stress calculation
    thanks in advance !!!
    .................................................. .................................................. .......
    clear
    rad = pi/180;
    r_p = 50;
    r_p2 = r_p;
    phi = 20*rad;
    P = 0.25;
    a = 1/P;
    d = 1.25/P;
    p = pi/P;
    t_p = p/2; % arc tooth thickness @ r_p ---- [mm]


    r_b = r_p*cos(phi); % base circle radius ----------- [mm]


    inv_phi = tan(phi)-phi; % derived angle ---------------- [rad]
    r = r_b:0.01:r_p+a;
    chi = acos(r_b./r); % pressure angle @ r ----------- [rad]
    inv_chi = tan(chi)-chi; % derived angle ---------------- [rad]
    t = 2*r.*((t_p/(2*r_p))+inv_phi-inv_chi);
    beta = t./(2*r);
    x = r.*sin(beta); % x-coor of tooth profile ------ [mm]
    y = (r.*cos(beta)); % y-coor of tooth profile ------ [mm]
    N = P*2*r_p; % number of teeth
    figure(1)
    clf
    hold on
    plot(x,y)
    grid on
    axis equal
    xlabel('x [mm]')
    ylabel('y [mm]')
    title('involute spur gear tooth profile')
    .................................................. .................................................. .........................
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