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 x = 0, ;
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 also applied to and 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'.


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