Writing y value of Curtate Trochoid in the function of x? The parametric equations of a trochoid are $x = Rt-d\sin(t)$ $y = R-d\cos(t)$ For $d < R$, there should be only one corresponding y value for every $x$ value. So can we express this equation as a form of y(x)? <

It's impossible to write $y=y(x)$ since this requires to solve the equation$$\sin t=at+b$$analytically for constants $a,b$ which is solvable only numerically.