Question

what does sin(x/2) equal?

Answer 1

in terms of what?

Answer 2

in terms of simplifying? eg. sin2x=2sinxcosx. So what is sin(x/2)?

Answer 3

well then it will be\[\sin \frac{x}{2}=2 \sin \frac{x}{4} \cos \frac{x}{4}\]am i right?

Answer 4

ye i hope so :P

Answer 5

:)

Answer 6

so then how would you solve cosx+3sin(x/2) -2 = 0 for 0<=x<=pi?

Answer 7

i think that will not be useful for this problem, better to write \(\cos x\) in terms of half angles

Answer 8

so can you explain?

Answer 9

see, we'r going to make a quadratic out of ur equation

Answer 10

u sure know the formula\[\cos 2x=\cos^2 x-\sin^2 x\]so\[\cos x=\cos^2 \frac{x}{2}-\sin^2 \frac{x}{2}\]

Answer 11

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\[1-2 \sin^2 \frac{x}{2}+3 \sin \frac{x}{2}-2=0\]

Answer 12

sin pi/2 is 1

Answer 13

if u let \(u=\sin \frac{x}{2}\) ur equation becomes\[-2u^2+3u-1=0\]which is easy to solve :) makes sense ?

Answer 14

yes
thanks very much :)

Answer 15

very welcome :)