Difference between revisions of "Manuals/calci/CIS"

Latest revision as of 16:03, 10 December 2018

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 $Sine$ function.
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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 *This function gives the CIS value.
 *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>.
+*<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> function.
-*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>;
-*So "Cis" abbreviates "Cos + i Sin".
+* <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>.
+==Examples==
+#CIS(45) = 0.5253219888177297+i 0.8509035245341184
+#CIS(180) = -0.5984600690578581-i-0.8011526357338304
+#CIS(90.53) = -0.838546204483341+ⅈ0.5448304901036493
+==Related Videos==
+{{#ev:youtube|v=qjT3XvS7Qno|280|center|Complex Exponential}}
+==See Also==
+*[[Manuals/calci/SIN | SIN]]
+*[[Manuals/calci/COS  | COS ]]
+==References==
+[http://mathworld.wolfram.com/Cis.html Complex Exponential]
+*[[Z_API_Functions | List of Main Z Functions]]
+*[[ Z3 |   Z3 home ]]