Question

Find the value of cos(7pi/12) using a half angle formula?

Answer 1

Half angle formula for cosine:
\[\huge \cos\left(\frac{x}{2}\right)=\sqrt{\frac{1+cosx}{2}}\]
Let's try to put our angle in this form.
\[\huge \cos \left(\frac{7\pi}{12}\right)=\cos \left(\frac{ (\frac{7\pi}{6}) }{ 2 }\right)\]

Answer 2

\[\huge =\sqrt{\frac{1+\cos\left(\frac{7\pi}{6}\right)}{2}}\]

Answer 3

From there, you just need to remember what the cos of 7pi/6 is, and simplify things down.

I forget whether or not you need to worry about the +/- of the square root.. 7pi/12 is in the second quadrant, so I suppose we want the negative root.