Changing from cartesian to polar

[CompStang]

Homework Statement

A particle moves in a two-dimensional orbit defined by:
x(t)= A(2\alphat-sin(\alphat)
y(t)= A(1-cos(\alphat)
a) Find the tangential acceleration a_t and normal acceleration a_n as a function of time where the tangential and normal components are taken with respect to the velocity.

Homework Equations

x''(t)= A\alpha^2sin(\alphat)
y''(t)= A\alpha^2cos(\alphat)

The Attempt at a Solution

I found both the velocity and acceleration for both x and y vectors given and realize that a(t)= x''(t)i\widehat{}+ y''(t)j\widehat{}
also I know that:
a(t)=a_nr\widehat{}+a_t\phi\widehat{}
So I need to find x" and y" in terms of polar to get the answe for a_n and a_t

 

[CompStang]

sorry all these alphas are not supposed to be raised to the power of there previous components. it is supposed to be for example x(t)=A(2*(alpha)*t-sin((alpha)*t)...and so on