asinh関数(逆双曲線正弦)、acosh関数(逆双曲線余弦)、atanh関数(逆双曲線正接)をそれぞれ使う。逆双曲線余弦(緑色)は定義域が x > 1、逆双曲線正接(青色)は定義域が -1 < x < 1 であることに注意。
> plot(0, 0, type = "n", xlim = c(-3, 3), ylim = c(-3, 3),
+ xaxs = "i", yaxs = "i", xlab = "x", ylab = "y")
> d <- seq(-3, 3, 0.001)
> lines(d, asinh(d), col = "red")
> d <- seq(1, 3, 0.001)
> lines(d, acosh(d), col = "green")
> d <- seq(-0.999, 0.999, 0.001)
> lines(d, atanh(d), col = "blue")
> abline(h = -3:3, v = -3:3, lty = "dotted")
> text(-2.9, 2.8, expression("y =" * sinh^-1 * "(x)"), adj = 0, col = "red")
> text(-2.9, 2.5, expression("y =" * cosh^-1 * "(x)"), adj = 0, col = "green")
> text(-2.9, 2.2, expression("y =" * tanh^-1 * "(x)"), adj = 0, col = "blue")

計算例は、以下のとおり。
> d <- seq(-0.8, 0.8, 0.4)
> for (i in 1:length(d)) cat(sprintf("asinh(%4.1f) = %f\n", d[i], asinh(d[i])))
asinh(-0.8) = -0.732668
asinh(-0.4) = -0.390035
asinh( 0.0) = 0.000000
asinh( 0.4) = 0.390035
asinh( 0.8) = 0.732668
> d <- 1:5
> for (i in 1:length(d)) cat(sprintf("acosh(%4.1f) = %f\n", d[i], acosh(d[i])))
acosh( 1.0) = 0.000000
acosh( 2.0) = 1.316958
acosh( 3.0) = 1.762747
acosh( 4.0) = 2.063437
acosh( 5.0) = 2.292432
> d <- seq(-0.8, 0.8, 0.4)
> for (i in 1:length(d)) cat(sprintf("atanh(%4.1f) = %f\n", d[i], atanh(d[i])))
atanh(-0.8) = -1.098612
atanh(-0.4) = -0.423649
atanh( 0.0) = 0.000000
atanh( 0.4) = 0.423649
atanh( 0.8) = 1.098612