Difference between revisions of "Manuals/calci/CIS"

Revision as of 15:13, 22 December 2016

CIS (Theta)

This function gives the CIS value.
CIS is another name for the complex exponential.
$Cis(x)=e^{ix}=Cosx+iSinx$ , where $Cos$ is the $Cosine$ function, $i$ is the imaginary unit and $Sin$ is the $Sine$ .
Also $Cos(x)={\frac {e^{ix}+e^{-ix}}{2}}$ ; $Sin(x)={\frac {e^{ix}-e^{-ix}}{2i}}$ and $i^{2}$ =-1.
So Failed to parse (syntax error): {\displaystyle "Cis"} abbreviates Failed to parse (syntax error): {\displaystyle "Cos + i Sin"} .

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 *CIS  is another name for the complex exponential.
 *<math>Cis(x)=e^{ix}=Cosx+i Sinx</math>, where <math>Cos</math> is the <math>Cosine</math> function,<math>i</math> is the imaginary unit and <math>Sin</math> is the <math>Sine</math>.
-*Also<math> Cos(x)= \frac{e^{ix}+e^{-ix}}{2}</math>;<math>Sin(x)=\frac{e^{ix}-e^{-ix}}{2i}</math> and <math>i^2</math>=-1.
+*Also <math> Cos(x)= \frac{e^{ix}+e^{-ix}}{2}</math>;<math>Sin(x)=\frac{e^{ix}-e^{-ix}}{2i}</math> and <math>i^2</math>=-1.
-*So "Cis" abbreviates "Cos + i Sin".
+*So <math>"Cis"</math> abbreviates <math>"Cos + i Sin"</math>.