How do you find exact value of #sin (pi/ 3)#?

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Answer 1 · 2016-07-24T03:04:37

#sin (pi/3) = sqrt(3)/2#

#pi/3# Radians #= 60# Degrees

#sin 60 = sqrt(3)/2#

To prove this consider an equilateral trigangle ABC of side 2 units as diagram below.

enter image source here Ref: "Quora" - With thanks

The bisector of angle A meets side BC at D which is the midpoint of BC.

By Pythagoras:
#AB^2 = AD^2 + DB^2#
#2^2 = AD^2 +1^2 -> AD = sqrt(4-1) = sqrt(3)#

Angle B = 60 Degrees
Therefore: #sin(60) = (AD)/(AB) = sqrt(3)/2#