A-Level Further Maths · Further Pure
Hyperbolic Functions
What is it
Hyperbolic functions (sinh, cosh, tanh) are defined using exponentials rather than circles, but behave remarkably similarly to their trigonometric counterparts, satisfying analogous identities and having comparable derivatives and integrals.
Why it matters
Hyperbolic functions appear throughout physics and engineering — describing the shape of a hanging cable (a catenary) or appearing in special relativity — and they provide elegant solutions to certain integrals that trigonometric substitution alone cannot easily reach.
Exam tip
Keep the exponential definitions of sinh and cosh handy when unsure of an identity — unlike ordinary trig identities, hyperbolic identities can always be re-derived quickly from their exponential definitions if memory fails.
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