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1.12: Inverse Euler formula

  • Page ID
    47198
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    Euler's formula gives a complex exponential in terms of sines and cosines. We can turn this around to get the inverse Euler formulas.

    Euler’s formula says:

    \[e^{it} = \cos (t) + i \sin (t) \nonumber \]

    and

    \[e^{-it} = \cos (t) - i \sin (t). \nonumber \]

    By adding and subtracting we get:

    \[\cos (t) = \dfrac{e^{it} + e^{-it}}{2} \nonumber \]

    and

    \[\sin (t) = \dfrac{e^{it} - e^{-it}}{2i}. \nonumber \]

    Please take note of these formulas we will use them frequently!


    This page titled 1.12: Inverse Euler formula is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Jeremy Orloff (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.