- #1
RJLiberator
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Homework Statement
Show that Ccos(wt+phi) = Acos(wt)+Bsin(wt)
Homework Equations
Trig identity that states cos(wt+phi) = cos(wt)cos(phi)-sin(wt)sin(phi)
The Attempt at a Solution
Ccos(wt+phi)=(Ccos(phi))cos(wt)+(-Csin(phi))sin(wt)
let A = Ccos(phi)
Let B = -Csin(phi)
Ccos(wt+phi) = Acos(wt)+Bsin(wt)
and done.
Is this as simple as I have shown? Or am I making a critical mistake in letting A = Ccos(phi) and B = -Csin(phi)?
Is there a more rigorous way of doing this that would be expected?
Since phi is a constant, C is a constant, I would think that this is a suitable way to prove that these two sides are equal, but I can't help but feel a bit weak here about this.