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The hyperbolic functions are related to a hyperbola is the same way the the circular functions are related to a circle.
So, while the points with coordinates [cos(t), sin(t)] generate the unit circle, their hyperbolic counterparts, [cosh(t) , sinh(t)] generate the right half of the equilateral hyperbola. Other circular functions (tan, sec, cosec and cot) also have their hyperbolic counterparts, as do the inverse functions.
An alternative, equivalent pair of definitions is:
cosh(x) = (ex + e-x)/2
and
sinh(x) = (ex - e-x)/2
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What are the types of trigonometric functions?
There are three types of trigonometric functions, they are: 1- Plane Trigonometric Functions 2- Inverse Trigonometric Functions and 3- Hyperbolic Trigonometric Functions
Use of hyperbolic functions?
If you hold a chain at both ends and let it hang loosely, the path of the chain follows the path of the hyperbolic cosine. (This is also the shape of the St. Lois Arch.) Also, the integrals of many useful functions. For example, if an object is falling in a constant gravitational field with air resistance, the velocity of the object as a function of time involves the inverse hyperbolic tangent.
What are the seven types of function?
There are infinitely many types of functions. For example: Discrete function, Continuous functions, Differentiable functions, Monotonic functions, Odd functions, Even functions, Invertible functions. Another way of classifying them gives: Logarithmic functions, Inverse functions, Algebraic functions, Trigonometric functions, Exponential functions, Hyperbolic functions.
What is an arc-hyperbolic function?
An arc-hyperbolic function is an inverse hyperbolic function.
When a variable appears in the denominator of one or more term of an equation?
It can. And does, for example, in the hyperbolic trigonometric functions. It can make the solution harder but there is no law that says that solutions must be easy!
