Relationship between e, sin and cos: Difference between revisions
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(New page: ==Converting from e to sin/cos== It is often useful when doing signal processing to understand the relationship between e, sin and cos. Sometimes difficult calculations involving even or o...) |
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==Converting from e to sin/cos== |
==Converting from e to sin/cos== |
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It is often useful when doing signal processing to understand the relationship between e, sin and cos. Sometimes difficult calculations involving even or odd functions of <math>e</math> can be greatly simplified by using the relationship to simplify things. |
It is often useful when doing signal processing to understand the relationship between e, sin and cos. Sometimes difficult calculations involving even or odd functions of <math>e</math> can be greatly simplified by using the relationship to simplify things. The relationship is as follows: |
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<math>e^{j \theta} = cos( \theta ) + j*sin( \theta ). </math> |
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==Converting from sin/cos to e== |
==Converting from sin/cos to e== |
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<math>cos( \theta ) = \frac{e^{j \theta}+e^{-j \theta}}{2}</math> |
<math>cos( \theta ) = \frac{e^{j \theta}+e^{-j \theta}}{2}</math> |
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<math>sin( \theta ) = \frac{e^{j \theta}-e^{-j \theta}}{2j}</math> |
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Revision as of 02:48, 13 February 2008
Converting from e to sin/cos
It is often useful when doing signal processing to understand the relationship between e, sin and cos. Sometimes difficult calculations involving even or odd functions of can be greatly simplified by using the relationship to simplify things. The relationship is as follows:
Converting from sin/cos to e
The reverse conversion is also often helpful:
