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

[Rubidium]

1. Homework Statement
(a) Show that A$$_{0}$$cos($$\omega$$t+$$\delta$$) can be written as A$$_{s}$$sin($$\omega$$t)+A$$_{c}$$cos($$\omega$$t), 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($$\omega$$t+$$\delta$$)
v$$_{<i>x</i>}$$=-$$\omega$$Asin($$\omega$$t+$$\delta$$)




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?