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

2\cos(3 x - 1 ) = \cos(3x) - \sin(3x )

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

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

Question

Here is a little more review concerning trig functions. Using the formula for sin() and cos() of the sum of two angles.

2\cos(3 x - 1 ) = \cos(3x) - \sin(3x )

2\sin(5 x - 3 ) = \cos(5x) + \sin(5x )

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