Integration using Euler's formula: Difference between revisions

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==Euler's formula==

Euler's formula states that

:<math>e^{ix} = \cos x + i\,\sin x.</math>

Substituting &minus;''x'' for ''x'' gives the equation

:<math>e^{-ix} = \cos x - i\,\sin x.</math>

These two equations can be solved for the sine and cosine:

:<math>\cos x = \frac{e^{ix} + e^{-ix}}{2}\quad\text{and}\quad\sin x = \frac{e^{ix}-e^{-ix}}{2i}.</math>