Use trig identities and trig table -->
#2sin^2 t = 1 - cos 2t#
#2cos^2 t = 1 + cos 2t#
Call #(3pi)/8 = t# --> #2t = (6pi)/8 = (3pi)/4# --> #cos 2t = - sqrt2/2#
In this case, we have:
#2sin^2 t = 1 + sqrt2/2 = (2 + sqrt2)/2#
#sin ((3pi)/8) = sin t = +- sqrt(2 + sqrt2)/2#
Since #sin ((3pi)/8)# is positive, take the positive value.
#2cos^2 t = 1 - sqrt2/2 = (2 - sqrt2)/2#
#cos ((3pi)/8) = cos t = +- sqrt(2 - sqrt2)/2#
Since #cos ((3pi)/8)# is positive, take the positive value.
#tan ((3pi)/8) = (sin t)/(cos t) = sqrt(2 + sqrt2)/sqrt(2 - sqrt2)#
#cot ((3pi)/8) = sqrt(2 - sqrt2)/sqrt(2 + sqrt2)#
#sec ((3pi)/8) = 1/(cos) = 2/sqrt(2 + sqrt2)#
#csc ((3pi)/8) = 1/(sin) = 2/sqrt(2 - sqrt2)#
