# How do you find the value of cos (pi)/6?

Jul 18, 2016

sqrt3/2

#### Explanation:

There are 2 ways, that don't need calculator
a. Trig table of special arc --> $\cos \left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}$
b. Use triangle trigonometry
Consider a right triangle ABH that is half of an equilateral triangle
ABC
Angle $A = \frac{\pi}{6} = {30}^{\circ}$, Angle $B = {60}^{\circ}$, Angle $H = {90}^{\circ}$
Leg $A H = \sqrt{3}$; Leg BH = 1, Hypotenuse AB = 2.
We have
$\cos A = \cos \left(\frac{\pi}{6}\right) = \frac{A H}{A B} = \frac{\sqrt{3}}{2}$

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Edit from r3ce:

I believe another option to also look at especially for precalculus if it's applicable is the unit circle. It's basically a picture of certain common values for sine and cosine for angles such as $\frac{\pi}{6}$ or $\frac{2 \pi}{3}$