# Express sin4x in terms of sinx?

1. Mar 7, 2006

### kgh0st

express sin4x in terms of sinx???

Alright so im working on my homework tonight (i'm in trig/calc), and I get everything done but the last problem. Anyways, Ive been working on this for a while now and I cant even get an idea of where to start. Anyways, he says we need to express sin4x in terms of sinx. Can anyone help me out as to how to do this?

2. Mar 7, 2006

### Tide

HINT:

$$\sin 4x = 2 \sin 2x \cos 2x$$

3. Mar 8, 2006

### VietDao29

I don't think sin(4x) can be expressed in terms of only sin(x). It can, however be expressed in terms of sin(x), and cos(x).
In general, sin(2nx), where n is a natural number that's greater than or equal to 1, can be expressed in terms of sin(x), and cos(x), but not sin(x) alone.
sin((2n + 1)x), n >= 0, however can be expressed in terms of only sin(x).

4. Mar 8, 2006

### daveb

Well, actually, it can, since cos(x) = +sqrt(1-sin^2(x))