1. ## help me out

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

2. 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)

3. If i know sin x = y from the trig table but i dont have sin (x/2), then????

4. 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 $\displaystyle \sin{\frac{x}{2}}$

5. Originally Posted by pomp
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 $\displaystyle \sin{\frac{x}{2}}$

Exactly

6. ok....
i know sin 45 = 1/sqrt 2
but i dont know sin 22.5
?????

7. By using trig tables you should be able to find it.

8. Originally Posted by SENTINEL4
By using trig tables you should be able to find it.
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 $\displaystyle \sin^2x=4(1-T)\cdot T=4T-4T^2$

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

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)

9. Originally Posted by jashansinghal
ok....
i know sin 45 = 1/sqrt 2
but i dont know sin 22.5
?????
OK I understand what you are asking now, you want to express $\displaystyle \sin{\frac{x}{2}}$ in some exact form, in terms of $\displaystyle \sin{x}$ ? In that case you need to use the half angle formula:

$\displaystyle 2 \sin^2{\frac{x}{2}} = 1 - \cos{x}$