AQA•A-Level•Further Maths
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Hyperbolic Functions
Hyperbolic functions, their inverses, and calculus
Practice 26 subtopics in Hyperbolic Functions. All questions match the AQA A-Level specification.
About Hyperbolic Functions
Hyperbolic Functions is a key topic in the AQA A-Level Further Mathsspecification. This topic covers hyperbolic functions, their inverses, and calculus.
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sinh x = (e^x - e^(-x))/2cosh x = (e^x + e^(-x))/2tanh x = sinh x / cosh xsech x, cosech x, coth xGraphs of hyperbolic functionsDomain and rangeEven and odd propertiesConnection to exponentialscosh^2 x - sinh^2 x = 1sech^2 x = 1 - tanh^2 xcosech^2 x = coth^2 x - 1Addition formulaeDouble angle formulaeOsborn's rulearsinh x = ln(x + √(x^2 + 1))arcosh x = ln(x + √(x^2 - 1))artanh x = (1/2)ln((1+x)/(1-x))Deriving inverse formulaeGraphs of inverse hyperbolic functionsd/dx(sinh x) = cosh xd/dx(cosh x) = sinh xd/dx(tanh x) = sech^2 xDerivatives of inverse hyperbolicsIntegration involving hyperbolic functionsIntegration using hyperbolic substitutionStandard integrals with inverse hyperbolics
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