0
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.
