What does sinh X mean?
hyperbolic sine function
Sinh is the hyperbolic sine function, which is the hyperbolic analogue of the Sin circular function used throughout trigonometry. Sinh[x] decreases exponentially as x approaches and increases exponentially as x approaches . Sinh satisfies an identity similar to the Pythagorean identity satisfied by Sin, namely .
What is sinh of infinity?
sinh(x) is zero for x = 0, and tends to infinity as x tends to infinity and to minus infinity as x tends to minus infinity; tanh(x) is zero for x = 0, and tends to 1 as x tends to infinity and to -1 as x tends to minus infinity.
What is the integral of sinh X?
Integral sinh(x) sinh x dx = cosh x + C.
What is sinh X formula?
sinh x = ex − e−x 2 . sinh 0 = e0 − e−0 2 = 1 − 1 2 = 0 .
Is sinh periodic?
Thus sinh z is periodic with period 2pi in arg z = theta#.
How do you differentiate Sinh?
(sinhx)′=(ex−e−x2)′=ex+e−x2=coshx,(coshx)′=(ex+e−x2)′=ex−e−x2=sinhx. We can easily obtain the derivative formula for the hyperbolic tangent: (tanhx)′=(sinhxcoshx)′=(sinhx)′coshx−sinhx(coshx)′cosh2x=coshx⋅coshx−sinhx⋅sinhxcosh2x=cosh2x−sinh2xcosh2x.
What is Sinh cosh?
This is a bit surprising given our initial definitions. Definition 4.11.1 The hyperbolic cosine is the function coshx=ex+e−x2, and the hyperbolic sine is the function sinhx=ex−e−x2. ◻ Notice that cosh is even (that is, cosh(−x)=cosh(x)) while sinh is odd (sinh(−x)=−sinh(x)), and coshx+sinhx=ex.
What is ArcSinh equal to?
ArcSinh is the inverse hyperbolic sine function. For a real number , ArcSinh[x] represents the hyperbolic angle measure such that . ArcSinh is defined for complex argument by . ArcSinh[z] has branch cut discontinuities in the complex plane. Related mathematical functions include Sinh, ArcCosh, and ArcSin.
Is Tanh the inverse of tan?
Tanh is the hyperbolic tangent function, which is the hyperbolic analogue of the Tan circular function used throughout trigonometry. The inverse function of Tanh is ArcTanh.
