Question

Find the exact value without a calculator

Answer 1

\[\tan(\frac{ \pi }{ 8 })\]

Answer 2

\[\large\rm \tan\left(\frac{\pi}{8}\right)\quad=\tan\left(\frac{\pi/4}{2}\right)\]

Answer 3

Do you have your Half-Angle Formula handy? :)

Answer 4

There are 'nice' angles and then there are not so nice ones.
'Nice' angles include Pi/4, whose tangent is simply 1; pi/3, whose sine is Sqrt(3) / 2, and so on.

Zepdrix has suggested that you re-write the given problem using the 'nice' angle Pi/4, whose tangent is 1, and the "half angle formula."

Would you mind looking up that formula?

Answer 5

\[\frac{ \cos \theta - 1 }{ \sin \theta }\]

Answer 6

Take a look at the following:

https://www.google.com/search?q=half+angle+formula&espv=2&tbm=isch&imgil=WlhzRehkuqV63M%253A%253BzfXNMUjP8C-5JM%253Bhttp%25253A%25252F%25252Fmarikafruscio.eu%25252Ff3b48ba9258dfb80f2dc3e41a56e95ae.html&source=iu&pf=m&fir=WlhzRehkuqV63M%253A%252CzfXNMUjP8C-5JM%252C_&biw=1360&bih=673&ved=0ahUKEwjHlej0qNnJAhWIKWMKHWwDDQMQyjcIMg&ei=PaVtVoeDEIjTjAPshrQY&usg=__6EPYtP1ZbMpjYxyEfqQg5yK1UPM%3D#imgrc=WlhzRehkuqV63M%3A&usg=__6EPYtP1ZbMpjYxyEfqQg5yK1UPM%3D

This lists various forms of the Half Angle Formula.

Answer 7

Which Half Angle Formula looks to be most easily applicable to the problem at hand?