Reference · Math

math.sinh

math.sinh(num) -> float

What it does

The hyperbolic sine of a number, as a float, as Python's math.sinh: (e^x - e^-x) / 2. It takes any number, but grows like math.exp, so a large one overflows. Its inverse is math.asinh.

Examples

print(math.sinh(0), math.sinh(1), math.sinh(-1))print(math.sinh(2), math.asinh(math.sinh(2)))

0.0 1.1752011936438014 -1.17520119364380143.626860407847019 2.0

Edge cases

• The function is odd: math.sinh(-x) is -math.sinh(x).
• 710 is about the largest input that fits a float; 711 is a range error, and so is -711.
• inf gives inf, -inf gives -inf, NaN gives NaN.
• math.tanh(x) is math.sinh(x) / math.cosh(x).

print(math.sinh(-2) == -math.sinh(2))print(math.isfinite(math.sinh(710)), math.isfinite(math.sinh(-710)))print(math.sinh(math.inf), math.sinh(-math.inf), math.sinh(math.nan))print(math.tanh(1) == math.sinh(1) / math.cosh(1))

truetrue trueinf -inf NaNtrue

Errors

A result past the largest float is a runtime error (a range error), not an error value: it stops the request, and ?? does not catch it. A value that is not a number is a runtime error too.

print(math.sinh(711))

line 1: `math.sinh`: math range error (711)

print(math.sinh(-711))

line 1: `math.sinh`: math range error (-711)

Chaining

print(1 | math.sinh)print([0, 1, 2] | map(math.sinh))

1.1752011936438014[0.0, 1.1752011936438014, 3.626860407847019]

See also

math.cosh, math.tanh, math.asinh, math.exp, math.sin

Edit this page on GitHub · every example's output was made by running it (tools/refcheck.mjs) · questions on Discord or r/quillo