<!DOCTYPE html>
<html>
<head>
<title>arccsch &mdash; Math</title>
<link rel="stylesheet" type="text/css" href="../style.css">
</head>

<body>

<script src="../../build/math.js"></script>
<script src="../../../mathcell/build/mathcell.js"></script>

<script src="https://cdn.jsdelivr.net/gh/mathjax/MathJax@2.7.5/MathJax.js?config=TeX-AMS_HTML"></script>

<p class="function"><a href=../../complex3D.asp?guess=arccsch(x)> arccsch( <i>z</i> ) </a></p>

<p>The inverse hyperbolic cosecant of <i>z</i> in Math. Defined by</p>

\[ \operatorname{arccsch} ( \operatorname{csch} z ) = z \]

<p>Real part on the real axis:</p>

<div class="mathcell" style="height: 4in">
<script>

var parent = document.currentScript.parentNode;

var id = generateId();
parent.id = id;

MathCell( id, [] );

parent.update = function( id ) {

  var p1 = plot( x => arccsch( complex(x) ).re, [-5,-.01] );
  var p2 = plot( x => arccsch( complex(x) ).re, [.01,5] );

  var config = { type: 'svg' };

  evaluate( id, [ p1, p2 ], config );

}

parent.update( id );

</script>
</div>

<p>Imaginary part on the real axis is zero.</p>

<p>Real part on the imaginary axis:</p>

<div class="mathcell" style="height: 4in">
<script>

var parent = document.currentScript.parentNode;

var id = generateId();
parent.id = id;

MathCell( id, [] );

parent.update = function( id ) {

  var p1 = plot( x => arccsch( complex(0,x) ).re, [-5,-.01] );
  var p2 = plot( x => arccsch( complex(0,x) ).re, [.01,5] );

  var config = { type: 'svg' };

  evaluate( id, [ p1, p2 ], config );

}

parent.update( id );

</script>
</div>

<p>Imaginary part on the imaginary axis:</p>

<div class="mathcell" style="height: 4in">
<script>

var parent = document.currentScript.parentNode;

var id = generateId();
parent.id = id;

MathCell( id, [] );

parent.update = function( id ) {

  var p = plot( x => arccsch( complex(0,x) ).im, [-5,5] );

  var config = { type: 'svg' };

  evaluate( id, [ p ], config );

}

parent.update( id );

</script>
</div>

<p>Real part on the complex plane:</p>

<div class="mathcell" style="width: 6in; height: 6in">
<script>

var parent = document.currentScript.parentNode;

var id = generateId();
parent.id = id;

MathCell( id, [] );

parent.update = function( id ) {

  var p = parametric( (x,y) => [ x, y, arccsch( complex(x,y) ) ], [-5,5,151], [-5,5,151],
                      { complexFunction: 're', colormap: 'complexArgument' } );

  var config = { type: 'threejs' };

  evaluate( id, [ p ], config );

}

parent.update( id );

</script>
</div>

<p>Imaginary part on the complex plane:</p>

<div class="mathcell" style="width: 6in; height: 6in">
<script>

var parent = document.currentScript.parentNode;

var id = generateId();
parent.id = id;

MathCell( id, [] );

parent.update = function( id ) {

  var p = parametric( (x,y) => [ x, y, arccsch( complex(x,y) ) ], [-5,5,151], [-5,5,151],
                      { complexFunction: 'im', colormap: 'complexArgument' } );

  var config = { type: 'threejs' };

  evaluate( id, [ p ], config );

}

parent.update( id );

</script>
</div>

<p>Absolute value on the complex plane:</p>

<div class="mathcell" style="width: 6in; height: 6in">
<script>

var parent = document.currentScript.parentNode;

var id = generateId();
parent.id = id;

MathCell( id, [] );

parent.update = function( id ) {

  var p = parametric( (x,y) => [ x, y, arccsch( complex(x,y) ) ], [-5,5,151], [-5,5,151],
                      { complexFunction: 'abs', colormap: 'complexArgument' } );

  var config = { type: 'threejs' };

  evaluate( id, [ p ], config );

}

parent.update( id );

</script>
</div>

<p>Related functions: &nbsp; <a href="csch.html">csch</a> &nbsp; <a href="arcsech.html">arcsech</a></p>

<p>Function category: <a href="../functions.html#hyperbolic">hyperbolic functions</a></p>

</body>
</html>