How do you use half angle formula evaluate #sin(-67.5)# and #cos (pi/2)#?

1 Answer
Nghi N.
Jul 17, 2015

Find #sin (-67.5) and cos (pi/2)#

Explanation:

Call sin (-67.5) = sin t --> cos 2t = cos (-135) = cos 135 = #-sqrt2/2#
Apply the trig identity: #cos 2t = 1 - 2sin^2 t#

#2sin^2 t = 1 + sqrt2/2 = (2 + sqrt2)/2#
#sin^2 t = (2 + sqrt2)/4#
#sin t = sin (-67.5) = +- sqrt(2 + sqrt2)/2#

Call #cos (pi/2) = cos y# --> #cos 2y = cos pi = - 1#
Apply trig identity: #cos 2y = 2cos^2 y - 1#
#- 1 = 2cos^2 y - 1 #-> #2cos^2 y = 0# -->
#cos y = cos (pi/2) = 0#

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