Hyperbolic {base} | R Documentation |
These functions give the obvious hyperbolic functions. They respectively compute the hyperbolic cosine, sine, tangent, arc-cosine, arc-sine, arc-tangent.
cosh(x) sinh(x) tanh(x) acosh(x) asinh(x) atanh(x)
cos
, sin
, tan
,
acos
, asin
, atan
.
Ceps <- .Machine$double.eps # ``Computer epsilon'' x <- rnorm(500) all(abs(cosh(x) - (exp(x) + exp(-x))/2) < 10*Ceps) all(abs(sinh(x) - (exp(x) - exp(-x))/2) < 10*Ceps) all(Mod(cosh(x) - cos(1i*x)) < 10*Ceps) all(Mod(sinh(x) - sin(1i*x)/1i) < 10*Ceps) all(abs(tanh(x)*cosh(x) - sinh(x)) < 10*Ceps) ## Inverse: all(abs(asinh(sinh(x)) - x) < 10*Ceps) x[abs(acosh(cosh(x)) - abs(x)) > 100*Ceps] #- imprecise for small x all(abs(atanh(tanh(x)) - x) < 100*Ceps) all(abs(asinh(x) - log(x + sqrt(x^2 + 1))) < 10*Ceps) cx <- cosh(x) all(abs(acosh(cx) - log(cx + sqrt(cx^2 - 1))) < 1000*Ceps)