sqrt3/2

There are 2 ways that don’t need calculator

a. Trig table of special arc –> ##cos (pi/6) = sqrt3/2##

b. Use triangle trigonometry

Consider a right triangle ABH that is half of an equilateral triangle

ABC

Angle ##A = pi/6 = 30^@## Angle ##B = 60^@## Angle ##H = 90^@##

Leg ##AH = sqrt3##; Leg BH = 1 Hypotenuse AB = 2.

We have

##cos A = cos (pi/6) = (AH)/(AB) = sqrt3/2##

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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 ##pi/6## or ##(2pi)/3##