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Trig

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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)

  • Trig - ,

    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

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