Calculus 11.1

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Hyperbolic Functions
Scottys Castle, Death Valley, CA
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Consider the following two functions
These functions show up frequently enough that
they have been given names.
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The behavior of these functions shows such
remarkable parallels to trig functions, that they
have been given similar names.
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Hyperbolic Sine
(pronounced cinch x)
Hyperbolic Cosine
(pronounced kosh x)
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Hyperbolic Tangent
tansh (x)
Hyperbolic Cotangent
cotansh (x)
Hyperbolic Secant
sech (x)
Hyperbolic Cosecant
cosech (x)
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Now, if we have trig-like functions, it follows
that we will have trig-like identities.
First, an easy one
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(This one doesnt really have an analogy in trig.)
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(No Transcript)
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Note that this is similar to but not the same as
There are several other identities in table A6.2
on page 619. I will give you a sheet with the
formulas on it to use on the test.
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Derivatives can be found relatively easily using
the definitions.
Surprise, this is positive!
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(quotient rule)
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All of the derivatives are similar to trig
functions except for some of the signs. Sinh,
Cosh and Tanh are positive. The others are
negative
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Integral formulas can be written from the
derivative formulas. (See the table on page 620.)
CHyperbolic
2nd
MATH
Or you can use the catalog.
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