Last modified on 14 December 2013, at 18:25

Fractals/trigonometric

How to compute itEdit

One can use Maxima CAS to find it :

(%i1) z: x+y*%i;
(%o1) %i*y+x
(%o2) %i*y+x
(%i3) realpart(sinh(z));
(%o3) sinh(x)*cos(y)
(%i8) trigrat(sinh(x));
(%o8) (%e^−x*(%e^(2*x)−1))/2
(%i11) expand(%);
(%o11) %e^x/2−%e^−x/2

sin(Z) =

 Real =  \sin(x)   ((\exp(y) + \exp(-y))/2)

 Imag = \cos(x)   ((\exp(y) - \exp(-y))/2)

cos(Z)

 Real =  \cos(x)   ((\exp(y) + \exp(-y))/2)

 Imag = -\sin(x)   ((\exp(y) - \exp(-y))/2)

sinh(Z)

 Real =  \cos(y)   ((\exp(x) - \exp(-x))/2)

 Imag = \sin(y)   ((\exp(x) + \exp(-x))/2)

cosh(Z)

 Real =  \cos(y)   ((\exp(x) + \exp(-x))/2)

 Imag = \sin(y)   ((\exp(x) - \exp(-x))/2)

ImagesEdit

See : commons:Category:Trigonometric maps

This image shows the Julia set of acomplex function of the form f(z)=a*sin(z), where a is a suitably chosen number in the interval (0,1).

See alsoEdit