Changing from cartesian to polar

[CompStang]

Homework Statement

A particle moves in a two-dimensional orbit defined by:
x(t)= A(2$$\alpha$$t-sin($$\alpha$$t)
y(t)= A(1-cos($$\alpha$$t)
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($$\alpha$$t)
y''(t)= A$$\alpha$$^2cos($$\alpha$$t)

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