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sinh (= hyperbolic sin) is just one of the hyperbolic functions, each represents an open-ended curve on an x-y plot. Besides being open-ended, the function also has to meet other criteria to be hyperbolic -- it can be formed with the intercept between a plane and a cone, for example.
Specifically, sinh x = (ex - e-x)/2. I got the following values from Microsoft Excel:
x sinh(x)
-10 -11013.23287
-9 -4051.541902
-8 -1490.478826
-7 -548.3161233
-6 -201.7131574
-5 -74.20321058
-4 -27.2899172
-3 -10.01787493
-2 -3.626860408
-1 -1.175201194
0 0
1 1.175201194
2 3.626860408
3 10.01787493
4 27.2899172
5 74.20321058
6 201.7131574
7 548.3161233
8 1490.478826
9 4051.541902
10 11013.23287
If you plot the columnar data in Excel, you will see the curve will go +infinity to the right of the y-axis and -infinity to the left (hence, open-ended), and has an odd symmetry (y(-x) = -y(x)).
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What is an arc-hyperbolic function?
An arc-hyperbolic function is an inverse hyperbolic function.
What is the integral of the hyperbolic cosine of x with respect to x?
∫ cosh(x) dx = sinh(x) + C C is the constant of integration.
Is sinh a trigonometric function?
Yes, but it is called a hyberbolic trigonometric function
What is hyperbolic functions?
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
What is the integral of 1 divided by the hyperbolic sine of x with respect to x?
∫ 1/sinh(x) dx = ln(tanh(x/2)) + C C is the constant of integration.
What is a hyperbolic sine?
sinh(x) = ½[ex-e-x]
What is the example of hyperbolic?
The equation of a hyperbolic function is y = sinh(x) or y = cosh(x), where sinh(x) represents the hyperbolic sine function and cosh(x) represents the hyperbolic cosine function. Hyperbolic functions are similar to trigonometric functions but are defined in terms of exponentials.
What is an arc-hyperbolic function?
An arc-hyperbolic function is an inverse hyperbolic function.
What is Osborn's rule?
It is used in hyperbolic functions; it's the rule to change a normal trig function into hyperbolic trig function. Example: cos(x-y) = cosx cosy + sinx siny Cosh(x-y) = coshx coshy - sinhx sinhy Whenever you have a multiplication of sin, you write the hyperbolic version as sinh but change the sign. also applied when: tanxsinx (sinx)^2 etc... Hope this helps you
What are sinhx?
It is a hyperbolic function.
What is the integral of the hyperbolic cosine of x with respect to x?
∫ cosh(x) dx = sinh(x) + C C is the constant of integration.
What is the integral of the hyperbolic sine of x with respect to x?
∫ sinh(x) dx = cosh(x) + C C is the constant of integration.
Is sinh a trigonometric function?
Yes, but it is called a hyberbolic trigonometric function
What is the integral of the hyperbolic cotangent of x with respect to x?
∫ coth(x) dx = ln(sinh(x))+ C C is the constant of integration.
What is hyperbolic functions?
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
What is an antihyperbolic function?
An antihyperbolic function is a mathematical term for an inverse hyperbolic function.
What is an arctanh?
An arctanh is the inverse hyperbolic tangent function.
