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somebody please help me!
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Posted by: INeedHelp
sin^2 x/2 = cosx
^2 is the superscript 2, means square, x/2 means x divided by 2, written in fraction form
i know that the answer is 1.23 and 5.05, but how the heck in the world you figure it out?
thanks
Posted by: Canis Lupus
I was wondering why I hated math so much ... now I remember why...
Posted by: ElmStreet
sin^2 x/2 = cosx
ok it's like this.
{sin (x/2)}^2 = cos x right?
tan x = (sin x) / (cos x) right?
you multipy tan x on each side to get rid of cos on right side.
Posted by: ElmStreet
now you have [{sin(x/2)}^2] * sinx/ cosx = sin x right?
you divide each side with sin x. then you get
[{sin(x/2)}^2] / cos X = 1
i think there is got to be a corelation between sin(x/2) and cos x look up your text book.
Posted by: ElmStreet
now it looks pretty stupid to go through all the procedures if you can do this jusy by dividing cos x on each side.
anyway. i thought of another way.
replace x/2 = k then x = 2k
so (sin k)^2 = cos 2k
and see if there is any correlation betweek sin x and cos 2x
Posted by: Gunslinger
There's a whole list of trig formulas that should help you solve this problem. I used to have them all memorized, but some of theme escape me now.
Look in your textbook for things like sum and difference formulas, and double and half angle formulas.
Posted by: N.W.A_Kid
I remember doing that stuff just 3 years ago...hell if I can remember any of it now 
Posted by: uh...ok
cos 2x = (cos x)^2 - (sin x)^2
Pretty important double angle formula.
The other one you need to know is sin2x = 2sinxcosx.
Once you know that, just use Elm's substitution and do the algebra.
-uh...ok
Posted by: INeedHelp
nevermind i got it
it's like this
sin^2 x/2 = cosx
first you use the half angle identity to change sin^2 x/2 to [radical(1-cosx)/2]^2 and then you get 1-cosx/2 = cosx, times each side by 2 you get 1 - cosx = 2 cosx move the -cosx over to the other side, you get 1 = 3cosx, 1/3 = cosx, x' = 1.23, since cos function is a positive in this case, the we'll put it in quatrant 1 and 4, so x = 1.23 and 5.05
Posted by: NightMage
uhm dude did you have to prove the identity or just find x? just that I've done the same thing after not reading what I was asked to do properly. that's all 
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