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

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

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Answer 1 · 2016-07-18T04:52:54

sqrt3/2

Explanation:

There are 2 ways, that don't need calculator
a. Trig table of special arc --> $cos (\frac{π}{6}) = \frac{\sqrt{3}}{2}$ $cos (pi/6) = sqrt3/2$
b. Use triangle trigonometry
Consider a right triangle ABH that is half of an equilateral triangle
ABC
Angle $A = \frac{π}{6} = 30^{\circ}$ $A = pi/6 = 30^@$ , Angle $B = 60^{\circ}$ $B = 60^@$ , Angle $H = 90^{\circ}$ $H = 90^@$
Leg $A H = \sqrt{3}$ $AH = sqrt3$ ; Leg BH = 1, Hypotenuse AB = 2.
We have
$cos A = cos (\frac{π}{6}) = \frac{A H}{A B} = \frac{\sqrt{3}}{2}$ $cos A = cos (pi/6) = (AH)/(AB) = sqrt3/2$

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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 $\frac{π}{6}$ $pi/6$ or $\frac{2 π}{3}$ $(2pi)/3$

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

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