Sine-Cosine-Exponential Identities

Useful in my Digital Signal Processing class...

  • \\cos x = \\mathrm{Re}\{e^{ix}\} ={e^{ix} + e^{-ix} \\over 2}
  • \\sin x = \\mathrm{Im}\{e^{ix}\} ={e^{ix} - e^{-ix} \\over 2i}.
  • e^{ix} = \\cos x + i \\sin x \\;
  • \\mathrm{sinc}(x) = \\frac{\\sin(\\pi x)}{\\pi x}.\\,\!

Source: Wikipedia - Euler's formula

Source: Wikipedia - Sinc function

blogroll

social