Difference between revisions of "Manuals/calci/CSCH"

Revision as of 00:22, 6 November 2013

CSCH(z)

This function gives the Hyperbolic Cosecant of 'z'.
It's also called as Circular function.
Here $CSCH=sinh(z)^{-1}$ ie, ${\frac {2}{e^{z}-e^{-z}}}$ or $-Icsc(iz)$ , where $i$ is the imaginary unit and $i={\sqrt {-1}}$
The relation between Hyperbolic & Trigonometric function is $CSC(iz)=-ICSCh(z)$ & $Csch(iz)=-iCsc(z)$
CSCH(-z)=-CSCH(z)

SINH(z)

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 ==Description==
-*This function gives the Hyperbolic SIN of 'z'.
+*This function gives the Hyperbolic Cosecant of 'z'.
 *It's also called as Circular function.
-*Here <math>SINH=\frac{e^z-e^{-z}}{2}</math> or <math>-iSIN(iz)</math>, where <math>i</math> is the imaginary unit and <math>i=\sqrt{-1}</math>
+*Here <math>CSCH= sinh(z)^{-1}</math> ie, <math>\frac{2}{e^z-e^{-z}}</math> or <math>-Icsc(iz)</math>, where <math>i</math> is the imaginary unit and <math>i=\sqrt{-1}</math>
-*The relation between Hyperbolic & Trigonometric function is <math>Sin(iz)=iSin(hz)</math> & <math>Sinh(iz)= iSin(z)</math>
+*The relation between Hyperbolic & Trigonometric function is <math>CSC(iz) = -ICSCh(z)</math> & <math>Csch(iz)=-iCsc(z)</math>
-*SINH(-z) = -SINH(z)
+*CSCH(-z)=-CSCH(z)
 == Examples ==