# finding the exact value

• Dec 30th 2009, 02:56 PM
alessandromangione
finding the exact value
sin 5 pal/8 i've tried almost every combination ( 5 pal/8 - pal/6, 4 ,3 ,2 ecc) and i'm still struggling..hope ui guys can help me
• Dec 30th 2009, 03:23 PM
skeeter
Quote:

Originally Posted by alessandromangione
sin 5 pal/8 i've tried almost every combination ( 5 pal/8 - pal/6, 4 ,3 ,2 ecc) and i'm still struggling..hope ui guys can help me

pal? do you mean pi , $\pi$ ?

note that $\frac{5\pi}{8}$ is one-half of $\frac{5\pi}{4}$

use the half-angle identity for sine ...

$\sin\left(\frac{t}{2}\right) = \pm \sqrt{\frac{1-\cos{t}}{2}}$
• Dec 30th 2009, 03:25 PM
pickslides
Did you mean $\sin\left(\frac{5\pi}{8}\right)$ ?

If so

$\sin\left(\frac{\theta}{2}\right)= \pm\sqrt{\frac{1-\cos(\theta)}{2}}$

Now make $\theta = \frac{5\pi}{4}$