Edexcel•A-Level•Further Maths
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Hyperbolic Functions
Definitions, identities, and calculus of hyperbolic functions
Practice 23 subtopics in Hyperbolic Functions. All questions match the Edexcel A-Level specification.
About Hyperbolic Functions
Hyperbolic Functions is a key topic in the Edexcel A-Level Further Mathsspecification. This topic covers definitions, identities, and calculus of hyperbolic functions.
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sinh x = (eˣ - e⁻ˣ)/2cosh x = (eˣ + e⁻ˣ)/2tanh x = sinh x / cosh xsech x, cosech x, coth xGraphs of hyperbolic functionsDomain and rangeEven/odd propertiescosh²x - sinh²x = 11 - tanh²x = sech²xcoth²x - 1 = cosech²xAddition formulaeDouble angle formulaeOsborn's rulearsinh x = ln(x + √(x²+1))arcosh x = ln(x + √(x²-1)), x ≥ 1artanh x = ½ln((1+x)/(1-x)), |x| < 1d/dx(sinh x) = cosh xd/dx(cosh x) = sinh xd/dx(tanh x) = sech²xDerivatives of inverse hyperbolics∫1/√(x²+a²)dx = arsinh(x/a) + c∫1/√(x²-a²)dx = arcosh(x/a) + cIntegration with hyperbolic substitutions
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