Friday, October 21, 2011

Hyperbolic Tangent & Hyperbolic Cotangent

Hyperbolic tangent is defined as

,

while hyperbolic cotangent is the reciprocal of hyperbolic tangent, and it is defined as


.

If we want to sketch the graph of the earlier function, think of the y-intercept and limits below:
  1. As , ;
  2. when ;
  3. as , .

If we want to sketch the graph of the later function, think of the limits below:
  1. As , ;
  2. as , ;
  3. as , ;
  4. as , .

The concept above applied for all values of a > 0. You may slide the value of 'a' below to look at the changes of and for different values of 'a'.


Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)


Betty, Created with GeoGebra

No comments:

Post a Comment