The arccosine of x is defined as the inverse cosine function of x when -1≤x≤1.
When the cosine of y is equal to x:
cos y = x
Then the arccosine of x is equal to the inverse cosine function of x, which is equal to y:
arccos x = cos^-1 x = y
Here cos-1 x means the inverse cosine and does not mean cosine to the power of -1.
acosh() Function in R
To calculate the hyperbolic arccosine in R, use the acosh() function. The inverse hyperbolic cosine function is defined by x == cosh(y). The acosh(x) returns the inverse hyperbolic cosine of the elements of x when x is a REAL scalar, vector, matrix, or array. The result has the same shape as x.
x: It is a numeric value, array, or vector.
Let’s calculate the acosh value of 1.
If you pass the 0 to the atanh() function, it will return 0.
Calculate acosh() of complex number
Define a complex value and pass that value to the acosh() function.
dt <- 8 + 9i acosh(dt)
Plot the acosh() function to a graph
dt <- seq(-1, 1, by = 0.01) plot(dt, acosh(dt), type = "l", col = "red")
Warning message: In acosh(dt) : NaNs produced
The function returns the NaN value that is why it can’t draw a graph based on that value.
Applying acosh() function to a Vector
To create a Vector in R, use the c() function. Then pass that vector to the acosh() function.
rv <- c(-1, 0.5, 0, 0.5, 1) acosh(rv)
 NaN NaN NaN NaN 0 Warning message: In acosh(rv) : NaNs produced
Passing a pi to the acosh() function
The pi is an inbuilt constant in R programming, and its value is 3.141593.
Let’s find the pi constant’s acosh() value.
Let’s see another example of pi.
acosh(pi / 4)
 NaN Warning message: In acosh(pi/4) : NaNs produced
That is it for acosh() function in R programming.