anonymous
  • anonymous
what does sin(x/2) equal?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
in terms of what?
anonymous
  • anonymous
in terms of simplifying? eg. sin2x=2sinxcosx. So what is sin(x/2)?
anonymous
  • anonymous
well then it will be\[\sin \frac{x}{2}=2 \sin \frac{x}{4} \cos \frac{x}{4}\]am i right?

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anonymous
  • anonymous
ye i hope so :P
anonymous
  • anonymous
:)
anonymous
  • anonymous
so then how would you solve cosx+3sin(x/2) -2 = 0 for 0<=x<=pi?
anonymous
  • anonymous
i think that will not be useful for this problem, better to write \(\cos x\) in terms of half angles
anonymous
  • anonymous
so can you explain?
anonymous
  • anonymous
see, we'r going to make a quadratic out of ur equation
anonymous
  • anonymous
u sure know the formula\[\cos 2x=\cos^2 x-\sin^2 x\]so\[\cos x=\cos^2 \frac{x}{2}-\sin^2 \frac{x}{2}\]
anonymous
  • anonymous
so \[\cos x=\color\red{\cos^2 \frac{x}{2}}-\sin^2 \frac{x}{2}=\color\red{1-\sin^2 \frac{x}{2}}-\sin^2 \frac{x}{2}=1-2 \sin^2 \frac{x}{2}\]put this in the equation\[1-2 \sin^2 \frac{x}{2}+3 \sin \frac{x}{2}-2=0\]
anonymous
  • anonymous
sin pi/2 is 1
anonymous
  • anonymous
if u let \(u=\sin \frac{x}{2}\) ur equation becomes\[-2u^2+3u-1=0\]which is easy to solve :) makes sense ?
anonymous
  • anonymous
yes thanks very much :)
anonymous
  • anonymous
very welcome :)

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