Proof of Elliptical Motion through R(t) Equation

[nna]

Homework Statement

Hi!, can anybody help me with this problem?

Proof that the position vector r(t) = A cos $$\omega$$t i + B sin ($$\omega$$t + $$\alpha$$) moves on an ellipse.

I understand that the parametric equation for an ellipse is x=a cos t & y=b sin t, but I just can't find any trigonometric identity that helps me. Do you know any math trick that could help me?

 

[ideasrule]

x=a cos t, y=b sin t is only for a canonical ellipse. If you find the general parametric equation for an ellipse, you'll see that your equation fits perfectly.

 

[nna]

I understood what you say, but the only thing I could see was that the ellipse is rotated, but I still don't know how to prove the statement