Hyperbolic Functions Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2005 Scotty’s Castle, Death Valley, CA

Consider the following two functions: These functions show up frequently enough that they have been given names.

The behavior of these functions shows such remarkable parallels to trig functions, that they have been given similar names.

Hyperbolic Sine: (pronounced “cinch x”) Hyperbolic Cosine: (pronounced “kosh x”)

Hyperbolic Tangent: “tansh (x)” Hyperbolic Cotangent: “cotansh (x)” Hyperbolic Secant: “sech (x)” Hyperbolic Cosecant: “cosech (x)”

First, an easy one: Now, if we have “trig-like” functions, it follows that we will have “trig-like” identities.

(This one doesn’t really have an analogy in trig.)

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.

Derivatives can be found relatively easily using the definitions. Surprise, this is positive!

(quotient rule)

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

Integral formulas can be written from the derivative formulas. (See the table on page 620.) Or you can use the catalog.  2nd MATH C:Hyperbolic On the TI-89, the hyperbolic functions are under: