Express sin4x in terms of sinx?

[kgh0st]

express sin4x in terms of sinx?

Alright so I am working on my homework tonight (i'm in trig/calc), and I get everything done but the last problem. Anyways, I've been working on this for a while now and I can't 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?

Thanks in advance.

 

[Tide]

HINT:

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

 

[VietDao29]

Alright so I am working on my homework tonight (i'm in trig/calc), and I get everything done but the last problem. Anyways, I've been working on this for a while now and I can't 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?

Thanks in advance.

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).

 

[daveb]

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