Hyperbolic Functions
 

Anyone here any good at hyperbolic functions and complex number?

Ive got a question that I'm struggling on...

Given that sinjA = jsinhA, show that the hyperbolic identity corresponding to sin3θ = 3sinθ - 4sin3θ is: sinh3A = 3sinh A + 4sinh3A by writing jA for θ

:shock:

](*,) ](*,) :help: :help: #-o

In mathematics, the hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions. The basic hyperbolic functions are the hyperbolic sine "sinh", and the hyperbolic cosine "cosh", from which are derived the hyperbolic tangent "tanh", etc., in analogy to the derived trigonometric functions. The inverse functions are the inverse hyperbolic sine "arsinh" (also called "arсsinh" or "asinh") and so on.

HTH
:D

Close but no cigar...

Thanks for the help but it needs to be rearranged using those identities somehow.

Cheers anyway

Try PMing Professor. He's a Professor of Mathematics.

Re: Hyperbolic Functions
 

Is that question right? should it be sin3θ = 3sinθ - 4sin^3θ (i.e. 4 sin cubed theta)?

yup, thats what I got in front of me. I got the answer except I cant get the -4sin3θ to + 4sin3θ

Re: Hyperbolic Functions
 

sin3θ = 3sinθ - 4sin^3θ

substituting jA for θ gives

sin3jA = 3sinjA - 4sin^3jA

since sinjA = jsinhA

jsinh3A = 3jsinhA - 4j^3sinh^3A

divding thorough by j gives

sinh3A = 3sinhA - 4j^2sinh^3A

but as j^2 = -1

sinh3A=3sinhA+4sinh^3A

Re: Hyperbolic Functions
 

Geek alert :shock:

Re: Hyperbolic Functions
 

:oops: :oops: :oops: