conversion into cartesian formula

Hello, i have the following polar formulapresented bellow, i am trying to convert into cartesian formula, the only way i thought was using "taylor" command to get even an approximated version,but its not working on polar formulas,"pol2cart" command only converts the points, where as i need only a cartesian formula expression of y=f(x) ,what should i do? Thanks

phi=0.87*sin((log(r)*pi)/(log(tau)));

[Alexandra Harkai]

Why would you need a different function from polar to Cartesian other than pol2cart? Is it the actual formula you're looking for or just a tool that does it?

Answer 1

[Star Strider]

It is not going to be an easy conversion. I would do a direct substitution (see the subs call for the substitutions I used), then solve it numerically. No analytic solution exists (at least that I can see).

The Code —

syms phi r tau x y
Eq = phi == 0.87*sin((log(r)*pi)/(log(tau)));
Eq = subs(Eq, {phi, r}, {atan(y/x), sqrt(x^2+y^2)})
Eq = simplify(expand(Eq), 'Steps',20)

Eq =
atan(y/x) == (87*sin((pi*log((x^2 + y^2)^(1/2)))/log(tau)))/100

Eq =
87*sin((pi*log(x^2 + y^2))/(2*log(tau))) == 100*atan(y/x)