### Hyperbolic Functions

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Definition of hyperbolic function. First Known Use of hyperbolic function circa , in the meaning defined above. Learn More about hyperbolic function. Share hyperbolic function Post the Definition of hyperbolic function to Facebook Share the Definition of hyperbolic function on Twitter. Resources for hyperbolic function Time Traveler!

## Parametric equations of hyperbola, hyperbolic functions defined in terms of exponential functions

Explore the year a word first appeared. Dictionary Entries near hyperbolic function hyperbolic cosecant hyperbolic cosine hyperbolic cotangent hyperbolic function hyperbolic geometry hyperbolic navigation hyperbolic paraboloid. Statistics for hyperbolic function Look-up Popularity.

Time Traveler for hyperbolic function The first known use of hyperbolic function was circa See more words from the same year. Comments on hyperbolic function What made you want to look up hyperbolic function? Get Word of the Day daily email!

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## Hyperbolic Functions Calculator

Ask the Editors On Contractions of Multiple Words You all would not have guessed some of these A Look at Uncommon Onomatopoeia Some imitative words are more surprising than others Literally How to use a word that literally drives some people nuts. One physical application of hyperbolic functions involves hanging cables. If a cable of uniform density is suspended between two supports without any load other than its own weight, the cable forms a curve called a catenary. The following figure shows chains hanging from a row of posts.

Figure 3. Chains between these posts take the shape of a catenary. Hyperbolic functions can be used to model catenaries. Determine the length of the cable in feet. For the following exercises, find the derivatives of the given functions and graph along with the function to ensure your answer is correct.

For the following exercises, find the antiderivatives for the given functions. What do you notice? Does this confirm your answer for the previous question?

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Apply the formulas for the derivatives of the inverse hyperbolic functions and their associated integrals. Describe the common applied conditions of a catenary curve. Figure 1. Graphs of the hyperbolic functions.

### MuPAD Functions

Hint Use the formulas in Figure and apply the chain rule as necessary. Calculus of Inverse Hyperbolic Functions Looking at the graphs of the hyperbolic functions, we see that with appropriate range restrictions, they all have inverses. Applications One physical application of hyperbolic functions involves hanging cables. Figure 4.

A hyperbolic cosine function forms the shape of a catenary. Show Solution Recall from Section 6. Show Solution [latex] Hint Use the procedure from the previous example.