How do you find the exact values of sin 75 degrees using the half angle formula?

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Nghi N. Share
Jul 15, 2015

Answer:

enter image source here Find: sin 75 deg
Answer: #sin 75 = +- sqrt(2 + sqrt3)/2#

Explanation:

Call sin 75 = sin t --> cos 150 = cos 2t
On the trig unit circle,
cos (150) = cos (180 - 30) = - cos 30 =# -(sqrt3)/2#
#cos 150 = (-sqrt3)/2 = 1 - 2sin^2 t#
#2sin^2 t = (2 + sqrt3)/2#

#sin (75) = sin t = +- (sqrt(2 + sqrt3))/2#

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