# Location of half angle

• Jan 11th 2011, 02:39 PM
IDontunderstand
Location of half angle
Sin u = 5/13 and pi/2<u<pi.

Find Sin (u/2); How do you determine the sign (positive or negative) for the value?

Using that information find cos (u/2): I have sqrt(26)/26. Is this positive or negative? How do I know?
• Jan 11th 2011, 02:47 PM
pickslides
Quote:

Originally Posted by IDontunderstand
Sin u = 5/13 and pi/2<u<pi.

Find Sin (u/2); How do you determine the sign (positive or negative) for the value?

Which quadrant will it be in?

for $\displaystyle \cos u$ consider pythagorean triplet 5,12,13.
• Jan 11th 2011, 02:48 PM
Plato
Quote:

Originally Posted by IDontunderstand
Sin u = 5/13 and pi/2<u<pi.

Find Sin (u/2); How do you determine the sign (positive or negative) for the value?

Using that information find cos (u/2): I have sqrt(26)/26. Is this positive or negative? How do I know?

$\displaystyle \cos\left(u\right)=\frac{-12}{13}$

$\displaystyle \sin\left(\frac{u}{2}\right)=\sqrt{\frac{1-\cos(u)}{2}}$
• Jan 11th 2011, 02:49 PM
skeeter
Quote:

Originally Posted by IDontunderstand
Sin u = 5/13 and pi/2<u<pi.

Find Sin (u/2); How do you determine the sign (positive or negative) for the value?

Using that information find cos (u/2): I have sqrt(26)/26. Is this positive or negative? How do I know?

if ...

$\displaystyle \displaystyle \frac{\pi}{2} < u < \pi$

then ...

$\displaystyle \displaystyle \frac{\pi}{4} < \frac{u}{2} < \frac{\pi}{2}$ ... quad I , correct?
• Jan 11th 2011, 03:06 PM
saravananbs
sin u =5/13 and pi/2<u<pi

so find cos u = -12/13 as it is in 2nd quadrant.

use cos u= 2$\displaystyle cos^2 u/2$ -1 to evaluate cos u/2.

you take only positive value as it is in 1st quadrant.

using that you can find sin u/2 also.

since u/2(pi/4<u/2<pi/2 ) is in 1st quadrant

both cos u/2 and sin u/2 are positive.
• Jan 11th 2011, 03:30 PM
Plato
@saravananbs
Why not learn to post in symbols? You can use LaTeX tags
You do understand that this is not a homework service?
$$\sin\left(\frac{u}{2}\right)=\sqrt{\dfrac{1-\cos(u)}{2}}$$
gives $\displaystyle \sin\left(\frac{u}{2}\right)=\sqrt{\dfrac{1-\cos(u)}{2}}$
• Jan 11th 2011, 03:46 PM
saravananbs
Quote:

Originally Posted by Plato
@saravananbs
Why not learn to post in symbols? You can use LaTeX tags
You do understand that this is not a homework service?
$$\sin\left(\frac{u}{2}\right)=\sqrt{\dfrac{1-\cos(u)}{2}}$$
gives $\displaystyle \sin\left(\frac{u}{2}\right)=\sqrt{\dfrac{1-\cos(u)}{2}}$

yes i try to use latex.

i have given only the approach to the problem.