# Hyperbolic function/R/Monotonicity properties/Fact

The function

hyperbolic sine is strictly increasing, and the function hyperbolic cosine

is strictly decreasing on and strictly increasing on . The function

hyperbolic sine is strictly increasing, and the function hyperbolic cosine

is strictly decreasing on ${}\mathbb {R} _{\leq 0}$ and strictly increasing on ${}\mathbb {R} _{\geq 0}$.