Question
Use the half-angle formulas to come up with an exact expression for each function value below. You do not have to simplify your answers.
cos(pi/16)
cos(pi/16)
Answers
drwls
cos (x/2) = sqrt[(1/2)(1 + cosx)]
cos(pi/16) = sqrt[(1/2)(1 + cos(pi/8)]
cos(pi/8) = sqrt[(1/2)(1 + cos(pi/4)]
= sqrt[(1/2)(1 + sqrt2/2] = 0.92388..
cos(pi/16) = sqrt[(1/2)*1.92388]
= 0.980785..
Writing it in exact form would be a bit messy, but I hope you see how it can be done
cos(pi/16) = sqrt[(1/2)(1 + cos(pi/8)]
cos(pi/8) = sqrt[(1/2)(1 + cos(pi/4)]
= sqrt[(1/2)(1 + sqrt2/2] = 0.92388..
cos(pi/16) = sqrt[(1/2)*1.92388]
= 0.980785..
Writing it in exact form would be a bit messy, but I hope you see how it can be done