Hyperbolic Functions 1 (AQA A-Level Further Maths): Flashcards

$\sinh x = \frac{e^x - e^{-x}}{2}$

$\cosh x = \frac{e^x + e^{-x}}{2}$

$\tanh x = \frac{\sinh x}{\cosh x}$

$\cosh^2 x - \sinh^2 x \equiv 1$

$(0, 1)$

$0$

$\ln(x + \sqrt{x^2 + 1})$

$\ln(x + \sqrt{x^2 - 1})$, $x \geq 1$

$-1 < y < 1$

Even function: $\cosh(-x) = \cosh x$