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...Chapter hyperbolic functions objectives after studying this you should understand what is meant by a function be able to find derivatives and integrals of inverse use them in calculus applications recognise logarithmic equivalents introduction will introduce the which may have noticed on your calculator with abbreviation hyp see some connections trigonometric various cannot found without help first systematic consideration was done swiss mathematician johann heinrich lambert definitions cosine written coshx defined for all real values x relation ex e similarly sine sinhx names these two suggest that they similar properties investigated activity show simplify multiplying expressions together cosh sinh b considering c terms exponential prove example y coshxcoshy sinhxsinhy solution coshy sinhy subtracting gives xcosh xsinh exercise following identities sinha sinhb cosha coshb bsinh osborn s rule from previous similarity between corresponding fact formulae can converted into using states ...