Writing expression in terms of t=tan x/2

**icesta1** · March 3rd 2010, 10:28 PM

Stuck on this one question.

3cosx + 4sinx, write in terms of t=tan x/2

The answer is 3 - 3t^2 +8t / 1+t^2

Sorry I just wrote it in normal text, in a hurry lol.

Thanks

**Grandad** · March 3rd 2010, 10:42 PM

Hello icesta1

Originally Posted by icesta1

Stuck on this one question.

3cosx + 4sinx, write in terms of t=tan x/2

The answer is 3 - 3t^2 +8t / 1+t^2

Sorry I just wrote it in normal text, in a hurry lol.

Thanks

Provided you know the formulae:

$\sin x = \frac{2t}{1+t^2}$ and $\cos x = \frac{1-t^2}{1+t^2}$

I don't see what the problem is. Just substitute these into the expression, and the answer follows immediately:

$3\cos x +4\sin x = \frac{3(1-t^2)}{1+t^2}+ \frac{8t}{1+t^2}$

$=\frac{3-3t^2+8t}{1+t^2}$

Have you seen these formulae before?

Grandad

**icesta1** · March 3rd 2010, 11:12 PM

Hm... its funny cause I actually have that written in my book lol. I think i might have been looking at the wrong answer while doing it >_< lol.

Thanks anyways

EDIT: Nvm i got it

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