Question

What's the exact value of cos(pi/12) using the half-angle formula?

Answer 1

Hey!

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Answer 2

\[\Large\bf\sf \cos\left(\frac{x}{2}\right)\quad=\quad \pm\sqrt{\frac{1+\cos x}{2}}\]Since pi/12 is in the first quadrant, we only want the `positive` square root.

Answer 3

\[\Large\bf\sf \cos\left(\frac{\pi}{12}\right)\quad=\quad \cos\left(\frac{\pi}{6\cdot 2}\right)\quad=\quad \cos\left(\frac{\pi/6}{2}\right)\]
\[\Large\bf\sf =\quad \sqrt{\frac{1+\cos \pi/6}{2}}\]
Lemme know if that second to last step was confusing.
I did a little trick with fractions.