Difference between revisions of "Manuals/calci/CIS"

Revision as of 14:13, 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 $Cis$ abbreviates $Cos+iSin$ .

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 *<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.
-*So <math>"Cis"</math> abbreviates <math>"Cos + i Sin"</math>.
+*So <math>Cis</math> abbreviates <math>Cos + i Sin</math>.