# Finding an expression for (e.g. sin (3x)) in terms of (e.g. sin x) alone?

liquidwater

## Homework Statement

Use double-angle and addition formulæ and other relations for trigonometrical functions to find an expression for sin(3x) in terms of sin x alone.

My problem is I don't know what is meant by "find an expression for sin(3x) in terms of sin x alone.". I know the relevant formulae but do not know what is actually wanted of the question. I know I can 'split' it by going sin(2x + x) then using addition formulae... But I don't know why or what is expected as a final answer. An equation involving only sin and no cos?

## The Attempt at a Solution

No idea.

Gold Member
Basically, what the question is asking you is to find another way to write sin(3x) using only sin(x). So your final answer cannot have any sin(3x) or sin(2x), but only sin(x).

I think your first idea is a good one:

$$sin(3x) = sin(2x + x) = sin(2x)cos(x) + cos(2x)sin(x)$$

However, this still has sin(2x), cos(2x) and cos(x) in it. How can you get rid of all these and be left with just a combination of sin(x)?

rs1n

## Homework Statement

Use double-angle and addition formulæ and other relations for trigonometrical functions to find an expression for sin(3x) in terms of sin x alone.

My problem is I don't know what is meant by "find an expression for sin(3x) in terms of sin x alone.". I know the relevant formulae but do not know what is actually wanted of the question. I know I can 'split' it by going sin(2x + x) then using addition formulae... But I don't know why or what is expected as a final answer. An equation involving only sin and no cos?

2. Then consider any formulas for $\sin(2x)$ and $\cos(2x)$? In particular, you will want the identity for $\cos(2x)$ that involves only $\sin x$ as there are three identities for $\cos(2x)$. And don't forget the most basic one: $(\sin x)^2 + (\cos x)^2 = 1$.

rs1n
Doh! Looks like I type too slowly at this early hour... Danago beat me to the punch!

liquidwater
Thanks a lot to both of you, I actually understand what is required now.

I'm a bit lost with actually getting the solution, but I really do need to work on my math skills so I'll do that.

Thanks again!

Gold Member
Give it a good shot, and if you get lost in the algebra and trig. identities, feel free to post back here and im sure someone will be able to help out All the best,
Dan.

Gold Member
Give it a good shot, and if you get lost in the algebra and trig. identities, feel free to post back here and im sure someone will be able to help out All the best,
Dan.