asinh
Symbolic inverse hyperbolic sine function
Syntax
Description
Examples
Inverse Hyperbolic Sine Function for Numeric and Symbolic Arguments
Depending on its arguments, asinh returns
floating-point or exact symbolic results.
Compute the inverse hyperbolic sine function for these numbers. Because these numbers
are not symbolic objects, asinh returns floating-point
results.
A = asinh([-i, 0, 1/6, i/2, i, 2])
A = 0.0000 - 1.5708i 0.0000 + 0.0000i 0.1659 + 0.0000i... 0.0000 + 0.5236i 0.0000 + 1.5708i 1.4436 + 0.0000i
Compute the inverse hyperbolic sine function for the numbers converted to symbolic
objects. For many symbolic (exact) numbers, asinh returns
unresolved symbolic calls.
symA = asinh(sym([-i, 0, 1/6, i/2, i, 2]))
symA = [ -(pi*1i)/2, 0, asinh(1/6), (pi*1i)/6, (pi*1i)/2, asinh(2)]
Use vpa to approximate symbolic results with floating-point
numbers:
vpa(symA)
ans = [ -1.5707963267948966192313216916398i,... 0,... 0.16590455026930117643502171631553,... 0.52359877559829887307710723054658i,... 1.5707963267948966192313216916398i,... 1.4436354751788103012444253181457]
Plot Inverse Hyperbolic Sine Function
Plot the inverse hyperbolic sine function on the interval from -10 to 10.
syms x fplot(asinh(x),[-10 10]) grid on
Handle Expressions Containing Inverse Hyperbolic Sine Function
Many functions, such as diff,
int, taylor, and
rewrite, can handle expressions containing
asinh.
Find the first and second derivatives of the inverse hyperbolic sine function:
syms x diff(asinh(x), x) diff(asinh(x), x, x)
ans = 1/(x^2 + 1)^(1/2) ans = -x/(x^2 + 1)^(3/2)
Find the indefinite integral of the inverse hyperbolic sine function:
int(asinh(x), x)
ans = x*asinh(x) - (x^2 + 1)^(1/2)
Find the Taylor series expansion of asinh(x):
taylor(asinh(x), x)
ans = (3*x^5)/40 - x^3/6 + x
Rewrite the inverse hyperbolic sine function in terms of the natural logarithm:
rewrite(asinh(x), 'log')
ans = log(x + (x^2 + 1)^(1/2))
Input Arguments
Version History
Introduced before R2006a
