Relationship between e, sin and cos - Revision history

Wilspa: /* Converting from e to sin/cos */

2008-02-13T11:02:07Z

Converting from e to sin/cos

← Older revision		Revision as of 04:02, 13 February 2008
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	==Converting from e to sin/cos==		==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 <math>e</math> can be greatly simplified by using the relationship to simplify things. The relationship is as follows:		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:
			<br>
	<br>		<br>
	<math>e^{j \theta} = cos( \theta ) + j*sin( \theta ). </math>		<math>e^{j \theta} = cos( \theta ) + j*sin( \theta ). </math>

Wilspa at 11:01, 13 February 2008

2008-02-13T11:01:48Z

← Older revision		Revision as of 04:01, 13 February 2008
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			* Back to [[User:Wilspa\|my page]]

Wilspa at 11:00, 13 February 2008

2008-02-13T11:00:09Z

@@ Line 1: / Line 1: @@
 ==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 <math>e</math> can be greatly simplified by using the relationship to simplify things. The relationship is as follows:
 <math>e^{j \theta} = cos( \theta ) + j*sin( \theta ). </math>
@@ Line 9: / Line 10: @@
 <math>sin( \theta ) = \frac{e^{j \theta}-e^{-j \theta}}{2j}</math>

Wilspa at 10:48, 13 February 2008

2008-02-13T10:48:15Z

← Older revision		Revision as of 03:48, 13 February 2008
Line 1:		Line 1:
	==Converting from e to sin/cos==		==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 <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:
			<math>e^{j \theta} = cos( \theta ) + j*sin( \theta ). </math>

	==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>

			<math>sin( \theta ) = \frac{e^{j \theta}-e^{-j \theta}}{2j}</math>

Wilspa: 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...

2008-02-13T10:44:45Z

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...

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 odd functions of <math>e</math> can be greatly simplified by using the relationship to simplify things.

==Converting from sin/cos to e==
The reverse conversion is also often helpful:

<math>cos( \theta ) = \frac{e^{j \theta}+e^{-j \theta}}{2}</math>