sinh() Function in R with Example

The hyperbolic functions are analogs of the circular function or the trigonometric functions. The hyperbolic function occurs in the solutions of linear differential equations, calculation of distance and angles in the hyperbolic geometry, Laplace’s equations in the cartesian coordinates.

Equation of sinh() function

The equation of the sinh() function is the following.

sinh() Function

The hyperbolic functions are defined within the algebraic expressions, including the exponential function (e^x) and its inverse exponential functions (e^-x), where e is the Euler’s constant.

sinh() Function in R

To calculate the hyperbolic sine value of the numeric value in R, use the sinh() function. The sinh() is an inbuilt mathematical R function that calculates the hyperbolic sine of the given value.




x: It is a numeric value.




[1] 0
[1] 1.175201

Calculate sinh() of complex number

Define a complex value and pass that value to the sinh() function.

d <- 5 + 1i


[1] 40.09217+62.44552i

Plot the sinh() function to a graph

We will use the seq() function to create a series of values and pass that to the plot() function, which will create a line chart using the sinh() function.

dt <- seq(-1, 1, by = 0.05)
plot(dt, sinh(dt), typ = "l", col = "red")
abline(v = 0, lty = 6, col = "blue")


Plot the sinh() function to a graph

Applying sinh() function to a Vector

To create a Vector in R, use the c() function. Then pass that vector to the sinh() function.

rv <- c(-1, 0.5, 0, 0.5, 1)


[1] -1.1752012 0.5210953 0.0000000 0.5210953 1.1752012

Passing a pi to the sinh() function

The pi is an inbuilt constant in R programming, and its value is 3.141593.

Let’s find the pi constant’s sinh() value.



[1] 11.54874

Let’s see another example of pi.

sinh(pi / 4)


[1] 0.868671

That is it for sinh() function in R programming.

See also

R atanh()

R tanh()

R cosh()

R atan()

R tan()

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