How do you find the exact values of sin^2(pi/6) using the half angle formula?

1 Answer
Alan P.
Jul 23, 2015

#sin^2(pi/6) = 1/4#

Explanation:

By the half angle formula
#color(white)("XXXX")##sin^2(theta/2) = 1/2(1-cos(theta))#

For #theta = pi/3#
we have
#color(white)("XXXX")##sin^2(pi/6) = 1/2( 1 - cos(pi/3))#

#color(white)("XXXX")##color(white)("XXXX")##=1/2(1 - 1/2)#

#color(white)("XXXX")##color(white)("XXXX")##= 1/4#

(of course, this assumes that you remembered #cos(pi/3) = 1/2# but didn't remember #sin(pi/6) = 1/2#).

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