What is the answer to cos (3pi/8)?

1 Answer
Nghi N.
Apr 5, 2016

#- (sqrt(2 - sqrt2)/2)#

Explanation:

Call #cos ((3pi)/8) = cos t# --> #cos 2t = cos ((3pi)/4) = -sqrt2/2#
Apply the identity;
#cos 2t = 2cos^2 t - 1 = - sqrt2/2#
#2cos^2 t = 1 - sqrt2/2 = (2 - sqrt2)/2#
#cos^2 t = (2 - sqrt2)/4#
#cos t = - (sqrt(2 - sqrt2))/2# --> since cos ((3pi)/4) is negative
Answer: #cos t = cos ((3pi)/4) = - (sqrt(2 - sqrt2))/2#

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