Express -2sin3x - 4cos3x as a single sine function

[Physics is Phun]

ok i have no idea how to do this, and I'm pretty sure I should.
i have to express this in terms of the general sine funtion

f(x) = -2sin3x - 4cos3x

I don't even know where to start

 

[sanitykey]

Expressions of that format $$a\sin x + b\cos x$$ can be rewritten in terms of a sine only for positive values of a and b.

However, you have negative values for a and b, so i'd start by multiplying throughout by -1.

Then you could say:

$$a\sin x + b\cos x \equiv R\sin(x - \alpha)$$

Expand the right hand side of the equation and equate coefficients to find R and alpha.

 

[Pyrrhus]

Work out a right triangle with -2 and -4, where the hypothenuse is $A = \sqrt{(-2)^2 + (-4)^2}$ directed an angle $\phi$.