What is the relationship between A_{c} and A_{s} in simple harmonic motion?

[Rubidium]

1. Homework Statement
(a) Show that A_{0}cos(\omegat+\delta) can be written as A_{s}sin(\omegat)+A_{c}cos(\omegat), and determine A_{s} and A_{c} in terms of A_{0} and \delta.
(b) Relate A_{c} and A_{s} to the initial position and velocity of a particle undergoing simple harmonic motion.




2. Homework Equations
x=Acos(\omegat+\delta)
v_{<i>x</i>}=-\omegaAsin(\omegat+\delta)




3. The Attempt at a Solution
I have absolutely no idea where to begin...please help! Thanks a bunch for whoever does!

 

[Astronuc]

Start with the trigonometric identity for cosine of the sum of two angles, e.g. cos (a+b) = cos a cos b - sin a sin b, and see where that leads.

The initial position and velocity are taken at t = t₀ or t = 0?

 

[Rubidium]

I got the first part by using the trig identity and then taking the derivative, except I don't know why I had to take the derivative but it worked out anyway so I did.
Now, if t=0 then that would make the sine portion of the position 0 and the cosine portion 1 so the initial position would equal Ac, right?
For velocity, what would I do with that or is my whole idea wrong?