Re: Trig questions Message #5 Posted by Karl Schneider on 22 Nov 2008, 3:02 p.m., in response to message #2 by Walter B
This is not a comment to Walter, but the Forum s/w will let me respond to this post (see "HTML glitch" above):
(BTW, I appended "#143984" to the URL to make this work)
Quote:
But when you look at the half angle identities, it goes square root, etc, so you end up with two solutions. How can that be an identity when the original operation has only one solution?
Sin A/2 = Sqrt (1cos A/2)
So how can the dual solution value be the same as just dividing the angle by two and taking the sine which only has one solution?
Don 
The difference between triplebar identity sign and the doublebar equation sign has been explained. Really, they are all identities, and should be consistently denoted.
The equation you listed:
Sin A/2 = Sqrt (1cos A/2)
is not really a halfangle formula, as both angles are the same. Make it "cos^{2} (A/2)" and it's correct, but only as a form of
sin^{2} x + cos^{2} x = 1
The equation should have been listed as
Sin A/2 = Sqrt ((1cos A)/2)
and your reference should have stated the proper sign of the square root, based on sector of the angle.
BTW, an angle "phi" resulting from an inversetrigonometric ("arc") function will range between 180^{o} > phi >= +180^{o}
 KS
Edited: 23 Nov 2008, 3:42 p.m. after one or more responses were posted
