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Trigonometric derivatives and roots of unity

  1. Sep 4, 2009 #1
    sin x.
    d(sin x)/dx = cos x.
    d(cos x)/dx = -sin x.
    d(-sin x)/dx = - cos x.
    d(-cos x)/dx = sin x.

    i^2 = -1.
    i^3 = -i
    i^4 = 1
    i^5 = i.

    I know there is a relationship between trig, the complex numbers, and exponential functions. Is there a relationship between the pattern shown here?
  2. jcsd
  3. Sep 4, 2009 #2


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    Google Eulers relationship.
  4. Sep 4, 2009 #3
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