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Hyperbolic Functions Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2005 Scotty’s 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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First, an easy one: Now, if we have “trig-like” functions, it follows that we will have “trig-like” identities.

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

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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.) Or you can use the catalog. 2nd MATH C:Hyperbolic On the TI-89, the hyperbolic functions are under:

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