Question

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

Answer 1

sqrt3/2

Explanation:

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`