Harmonic Form

I need help with a question, I've done most of it.

"Given that y=e^-x sin2x, show that dy/dx can be expressed in the form R e^-x cos(2x + α). Find, to 3 significant figures, the values of R and α, where 0 < α < π/2."

I got the differentiated part to "-e^-x sin2x + 2e^-x cos2x" which is where i begin to use the harmonic form.

I also got α = to 26.6° but finding R is a real pain. Mainly because I can't get rid of the "x" power.

Can anyone help?

No?

No.

the "x" power is what gives the x-men their abilities... if you get rid of it we'll be defenceless!

yea

too complicated for the wannabe mathfags here

This can be solved just by using sum of angle identities:

Starting with the form you're finding for...
Re^-x*cos(2x + a) = Re^-x*(cos(2x)cos(a) - sin(2x)sin(a))

Setting equal to where you're coming from...
Re^-x*(cos(2x)cos(a) - sin(2x)sin(a)) = e^-x*(2cos(2x)-sin(2x))
R(cos(2x)cos(a) - sin(2x)sin(a)) = (2cos(2x)-sin(2x))
Rcos(2x)cos(a) - 2cos(2x) = Rsin(2x)sin(a)-sin(2x)
cos(2x)(Rcos(a)-2) = sin(2x)(Rsin(a)-1)

sin and cos are linearly independent, the constant term must be 0 =>
Rcos(a)- 2 = 0 => R = 2/cos(a)
Rsin(a) - 1 = 0 => R = 1/sin(a)

OP Here: I solved it and you're wrong 7, R equals sq root of 5.

>>8
R = sqrt(5) satisfies the system of equations given, so 7 is right.

No 7 is wrong.

>>10
Explain.

An A-Level mark scheme says so.

Proof by authority is fail.

>>1
HEY RETARD
IF ALPHA IS BETWEEN 0 AND PI HALVES, DON'T GIVE YOUR ANSWERS IN DEGREES