Question

use the half angle formulas to come up with an exact expression for each function value below. you do not have to simplify your answer
tan(pi/16)

Answer 1

well, pi/8 is 45 deg, so u can use \[\tan \theta/2=( 1-\cos \theta) / \sin \theta \]
and get an answer
\[\cos \pi/8=\sin \pi/8 =1/\sqrt{2}\] (using pythgoras)

Answer 2

Last time I checked, it was \(\cos \dfrac{\pi}{4} = \dfrac{1}{\sqrt 2}\) ;). You need to apply the half angle formula twice.

Answer 3

cool tnx. that's a good reason to change pi to tau (2pi)
http://www.youtube.com/watch?v=jG7vhMMXagQ