Here is a little more review concerning trig functions. Using the formula for sin() and cos() of the sum of two angles.

$4\cos(3 x + 1 ) =$ $\cos(3x)$ - $\sin(3x )$

$4\sin(3 x + 3 ) =$ $\cos(3x)$ + $\sin(3x )$

Now reverse this formula and given the expanded version find the version with just one term. This involves solving a pair of equations --
in order to get $A\cos(x) + B\sin(x) = R\sin(x+b) = R\sin(b)\cos(x) + R\cos(b)\sin(x)$ what values must you choose for $R$ and $b$? (Match coefficients.)

By convention we'll assume that the amplitude (the first coefficient on the left hand side) is positive.

$\cos(3 x +$ $) =$ $5\cos(3x)$ + $-2 \sin(3x )$

$\sin(3 x +$ $) =$ $6\cos(3x)$ + $-1 \sin(3x )$

The upshot of this exercise is that we can always rewrite the sum of multiples of sin() and cos() as a single sin() function with a given amplitude and phase shift. We could also write it as a single cos(), but it would have a different phase in that case. We'll use this many times in interpreting results.