# Writing expression in terms of t=tan x/2

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• Mar 3rd 2010, 10:28 PM
icesta1
Writing expression in terms of t=tan x/2
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
• Mar 3rd 2010, 10:42 PM
Grandad
Hello icesta1
Quote:

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:
$\displaystyle \sin x = \frac{2t}{1+t^2}$ and $\displaystyle \cos x = \frac{1-t^2}{1+t^2}$
I don't see what the problem is. Just substitute these into the expression, and the answer follows immediately:
$\displaystyle 3\cos x +4\sin x = \frac{3(1-t^2)}{1+t^2}+ \frac{8t}{1+t^2}$
$\displaystyle =\frac{3-3t^2+8t}{1+t^2}$
Have you seen these formulae before?

Grandad
• Mar 3rd 2010, 11:12 PM
icesta1
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