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Category > Geometry Posted 30 Oct 2017 My Price 15.00

Half Angle Formula

$\cos (\frac{θ}{2}) = \pm \sqrt{\frac{1 + \cos θ}{2}}$

First, since $105^{\circ}$

is the 2nd quadrant, cosine is negative, so by the half angle formula above,

$\cos (105^{\circ}) = \cos (\frac{210^{\circ}}{2}) = - \sqrt{\frac{1 + \cos (210^{\circ})}{2}}$

by $\cos (210^{\circ}) = - \frac{\sqrt{3}}{2}$

$= - \sqrt{\frac{1 - \frac{\sqrt{3}}{2}}{2}} = - \sqrt{\frac{2 - \sqrt{3}}{4}} = - \frac{\sqrt{2 - \sqrt{3}}}{2}$

I hope that this was helpful.

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