If i know $\displaystyle \sin x$ then how can we find $\displaystyle \sin(\frac{x}{2})$(Wondering)(Thinking)(Itwasntme)

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- Jul 24th 2009, 02:19 AMjashansinghalhelp me out
If i know $\displaystyle \sin x$ then how can we find $\displaystyle \sin(\frac{x}{2})$(Wondering)(Thinking)(Itwasntme)

- Jul 24th 2009, 02:36 AMSENTINEL4
Maybe one way is that if you have sinx=y , where y is a number, find from the tables for which x you have y.

Then if you find x, find x/2 and from the tables again find sin(x/2) - Jul 24th 2009, 02:38 AMjashansinghal
If i know sin x = y from the trig table but i dont have sin (x/2), then????

- Jul 24th 2009, 02:42 AMpomp
If you know $\displaystyle \sin{x}$ then you know $\displaystyle x$, if you know $\displaystyle x$ you know $\displaystyle \frac{x}{2}$ , if you know $\displaystyle \frac{x}{2}$ then you know $\displaystyle \sin{\frac{x}{2}}$

- Jul 24th 2009, 02:47 AMSENTINEL4
- Jul 24th 2009, 02:48 AMjashansinghal
ok....

i know sin 45 = 1/sqrt 2

but i dont know sin 22.5

????? - Jul 24th 2009, 02:59 AMSENTINEL4
By using trig tables you should be able to find it.

- Jul 24th 2009, 03:00 AMMoo
Is there 22.5 in a trig table ? -_-

Note that since 45 is in the first quadrant, 45/2 is also in the first quadrant.

We know that $\displaystyle \sin x=2\cos\tfrac x2\sin\tfrac x2$

So $\displaystyle \sin^2x=4\cos^2\tfrac x2\sin^2\tfrac x2$

Let $\displaystyle T=\sin^2\tfrac x2$

Then $\displaystyle \sin^2x=4(1-T)\cdot T=4T-4T^2$

This is a quadratic equation. In your situation, we have :

$\displaystyle 4T^2-4T-\frac 12=0$

Solve for T, by remembering it's positive (because it's a square)

And then take its square root, by remembering that it must be positive (because x/2 is in the first quadrant) - Jul 24th 2009, 03:00 AMpomp