Half angle identity for cos 13pi / 12

Question

anonymous · Answer

in degree or radian

mathmale · Answer

"Half angle identity for cos 13pi / 12  " comes across as vague?  I'm not really sure what yu want to calculate/determine/find.    Would you mind going back to the original source of this problem statement and double check to ensure that you've included everything?

anonymous · Answer

cos (13 Π /12 ) 

= cos [(12 Π + Π)/12 ] 

= cos(Π + Π/12) 

= - cos(Π/12) 

= - cos [Π/3 - Π/4 ] 

= - [ cos (Π/3) cos(Π/4) + sin(Π/3)sin(Π/4) 

= - [ (1/2)(1 /√2) + (√3/2)(1/√2) ] 

= - [ 1 + √3 ] / 2√2 

= - (1/4)(√2 + √6)

anonymous · Answer

= -(√6 + √2)\8
is the half angel

mathmale · Answer

I suspect that you were asked to use the "half angle formula for the cosine" in arriving at a solution to this problem (finding the cos of the given angle). Please see the attached illustration, which comes from http://www.purplemath.com/modules/idents.htm.

mathmale · Answer

The cosines of pi/2, pi/3, pi/6, and so on, are easily found,  Not so easily found is the cosine of pi/12.  this is the reason for using the "half angle formula" for the cosine.  Try this, please.