Is it possible to write all of the functions in terms of polar form?

Question

Is it possible to write all functions in terms of polar form?
For example, the equation of the circle with radius one can be written like $r=1$
I'm wondering whether reform the equations of all curves and write all functions with respect to $r$?

Answer 1

Yes and no. If you have a Cartesian function, it does not necessarily have to be definable explicitly, but no matter what the function is, you can always convert it to polar form using the fairly simple algorithm of taking each cartesian ordered pair $(x,y)$ and saying that $x^2+y^2 = r^2$ which gives you your $r$ value, and then using $r$ with your $x$ value in the algorithm $x=r\cos(\theta)$ which should give you a polar ordered pair $(r,\theta)$ so this will not necessarily give you an explicit polar, but it will convert any function to a polar.