Real world uses of hyperbolic trigonometric functions
2017年1月27日 · Among many uses and applications of the logistic function/hyperbolic tangent there are: Being an activation function for Neural Networks. These are universal function approximators that are pretty much becoming central to modern A.I. The Fermi-Dirac Distribution and Ising Model in statistical mechanics
Why are the hyperbolic functions defined the way they are?
2020年2月7日 · Significance of Hyperbolic functions: Hyperbolic functions are analogs of the ordinary trigonometric functions defined for the hyperbola rather than on the circle: just as the points $(\cos t, \sin t)$ form a circle with a unit radius $~(x^2+y^2=1)~$, the points $(\cosh t, \sinh t)$ form the right half of the equilateral hyperbola $~(x^2-y^2=1 ...
The interconnection between Hyperbolic functions and Euler's …
2018年7月16日 · It is called sinh because it is the hyperbolic equivalent of sine. It is called cosh because it is the hyperbolic equivalent of cosine. There is an interesting function, called the Gudermannian function that ties the circular and the hyperbolic functions together without using complex numbers.
When Hyperbolic function is zero? - Mathematics Stack Exchange
2015年9月7日 · The hyperbolic functions are quite different from the circular ones. For one thing, they are not periodic. For your equation, the double-"angle" formula can be used: $\sinh x \cosh x = 0$ $\frac 12 \sinh 2x = 0$ $\sinh 2x = 0$ The only solution to that is $2x = 0 \implies x = 0$.
Inverse Hyperbolic function - Mathematics Stack Exchange
2015年8月5日 · Find all values of following inverse hyperbolic trig function. 5. Solving hyperbolic functions. 0.
Connection between hyperbola and hyperbolic functions
2020年5月23日 · The hyperbolic angle is not included between any two lines. $$ \theta_h= A/a^2 = \frac12\; \log (\tan(π/4+θ_e)):$$ This area relation is found by direct integration. It is difficult for me to justify full cross-validity without going into definitions of lengths and hence the dependent hyperbolic angles in any one model of the hyperbolic ...
How were hyperbolic functions derived/discovered?
2018年4月18日 · How were Hyperbolic functions derived/discovered? Note that the above is an explanation of how you can interpret these functions, and how you can see the relation to the exponential function. It is by no means a historic explanation about how these things were first discovered. I don't know enough math history to answer that question.
statistics - How can I fit a set of data points to a hyperbola, a ...
2019年12月19日 · Moreover by comparing to the above linear regression, one see that the RMSE is almost not improved when going from linear regression to hyperbolic regression. So, in this case of large scatter it is of no interest to fit an hyperbolic function instead of a simple linear function. NOTE : From inspection, one point: $(0.9,3.4)$ appears as an ...
Proof of Hyperbolic Functions - Mathematics Stack Exchange
2015年4月25日 · Find the proof: (a) Use the definitions cosh(x)= 1/2(ex +e^−x) , sinh(x)= 1/2(e^x − e^−x) to express sinh(x + y) and cosh(x + y) in terms of cosh(x), sinh(x), cosh(y) and sinh(y).
Limit of hyperbolic function - Mathematics Stack Exchange
2015年7月11日 · Limit of function of hyperbolic. 6. An inequality involving hyperbolic sine functions. 1.