# Ch5 - Ch.5 PHYS2004 Quantitative Methods for Basic Physics...

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Ch.5 PHYS2004 Quantitative Methods for Basic Physics I (1 st Term 10/11) 1 Chapter 5 Transcendental Functions 5.1 Transcendental Functions By definition,  yfx is an algebraic function of x if it is a function that satisfies an irreducible algebraic equation of the form:       1 01 1 0 nn Pxy Pxy P xy Px  , (5.1.1) where n is a positive integer and   0 Px ,   1 , … are polynomials in x . A function that is not algebraic is called transcendental . Examples: Exponential and logarithmic functions: x e (   exp x ) and ln x (log e x ). Trigonometric and inverse trigonometric functions: sin x , cos x , tan x , cot x , sec x and csc x . 1 sin x , 1 cos x , 1 tan x , 1 cot x , 1 sec x and 1 csc x . Hyperbolic and inverse hyperbolic functions: sinh x , cosh x , tanh x , coth x , sech x and csch x . 1 sinh x , 1 cosh x , 1 tanh x , 1 coth x , 1 sech x and 1 csch x . 5.1.1 Hyperbolic and Inverse Hyperbolic Functions The two basic hyperbolic functions: sinh 2 x x ee x , and cosh 2 x x x ; ( 5 . 1 . 2 )

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Ch.5 PHYS2004 Quantitative Methods for Basic Physics I (1 st Term 10/11) 2 and the others can be defined as: sinh tanh cosh x x x x x ee x x  , and 1 coth tanh x x x x x x ; (5.1.3) 12 sech cosh x x x x , and csch sinh x x x x . (5.1.4) These functions are called hyperbolic because the locus defined by cosh sinh x at y , ( 5 . 1 . 5 )
Ch.5

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Ch5 - Ch.5 PHYS2004 Quantitative Methods for Basic Physics...

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