Mathematics Dictionary Dr. K. G. Shih

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Hyperbolic and trigonometric function

Subjects

Symbol Defintion Example : 2*3 means 2 times 3 Q00 | - hypergeometry : Tempory location Q01 | - Comparison of hyperbolic with trigonometric function : Graphics Q02 | - Comparison of hyperbolic with trigonometric function : Deifintion Q03 | - Comparison of hyperbolic with trigonometric function : Identity Q04 | - Q05 | - Q06 | - Q07 | - Q08 | - Q09 | - Q10 | -

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Answers

Q01. Comparison of hyperbolic with trigonometric function : Graphics Graphic Calculator Trigonometric functions and hyperbolic functions Method to use Start the garphic calculator Select run at current location Select yes Click Menu Click subject trigonometric function in upper box Click y = sin(x) in lower box to see the diagram Click back command at left side Click subject hyperbolic function in upper box Click y = sinh(x) in lower box to see the diagram Home work Compare the graphs of y = sin(x) and y = sinh(x) List the similarity and difference Go to Begin

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Q02. Comparison of hyperbolic with trigonometric function : Defintions

Go to Begin

sin(A) = y/r cos(A) = y/r tnn(A) = y/x = sin(A)/cos(A) csc(A) = r/y = 1/sin(A) sec(A) = r/y = 1/cos(A) cot(A) = x/y = 1/tan(A)

sinh(x) = (exp(x) - exp(-x))/2 cosh(x) = (exp(x) + exp(-x))/2 tnnh(x) = sinh(A)/cosh(A) csch(x) = 1/sinh(A) sech(x) = 1/cosh(A) coth(x) = 1/tanh(A)

Q03. Comparison of hyperbolic with trigonometric function : Identity

Go to Begin

cos(x)^2 + sin(x)^2 = 1 tan(x)^2 + 1 = sec(x)^2 cot(x)^2 + 1 = csc(x)^2 sin(-x) = -sin(x) cos(-x) = +cos(x) tan(-x) = -tan(x) cos(x+y) = cos(x)*cos(y) - sin(x)*sin(y) sin(x+y) = sin(x)*cos(y) + cos(x)*sin(y) tan(x+y) = (tan(x) + tan(y))/(1 + tan(x)*tan(y))

cosh(x)^2 - sinh(x)^2 = 1 1 - tanh(x)^2 = sech(x)^2 1 - coth(x)^2 = csch(x)^2 sinh(-x) = -sinh(x) cosh(-x) = +cosh(x) tanh(-x) = -tanh(x) cosh(x+y) = cosh(x)*cosh(y) + sinh(x)*sinh(y) sinh(x+y) = sinh(x)*cosh(y) + cosh(x)*sinh(y) tanh(x+y) = (tanh(x) + tanh(y))/(1 + tanh(x)*tanh(y))

Q04. Comparison of hyperbolic with trigonometric function : Derivative

Go to Begin

d/dx(sin(x)) = +cos(x) d/dx(cos(x)) = -sin(x) d/dx(tan(x)) = +sec(x)^2

d/dx(sinh(x)) = +cosh(x) d/dx(cosh(x)) = +sinh(x) d/dx(tanh(x)) = +sech(x)^2

Q05. Answer Go to Begin Q06. Answer Go to Begin Q07. Answer Go to Begin Q08. Answer Go to Begin Q09. Answer Go to Begin Q10. Answer Go to Begin Q00. Hypergeometry Temporary location Subject | Hypergeometry Go to Begin

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