[<< wikibooks] Fractals/trigonometric
= How to compute it =
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) =

R
e
a
l
=
sin
⁡
(
x
)
(
(
exp
⁡
(
y
)
+
exp
⁡
(
−
y
)
)

/

2
)

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

I
m
a
g
=
cos
⁡
(
x
)
(
(
exp
⁡
(
y
)
−
exp
⁡
(
−
y
)
)

/

2
)

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

cos(Z)

R
e
a
l
=
cos
⁡
(
x
)
(
(
exp
⁡
(
y
)
+
exp
⁡
(
−
y
)
)

/

2
)

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

I
m
a
g
=
−
sin
⁡
(
x
)
(
(
exp
⁡
(
y
)
−
exp
⁡
(
−
y
)
)

/

2
)

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

sinh(Z)

R
e
a
l
=
cos
⁡
(
y
)
(
(
exp
⁡
(
x
)
−
exp
⁡
(
−
x
)
)

/

2
)

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

I
m
a
g
=
sin
⁡
(
y
)
(
(
exp
⁡
(
x
)
+
exp
⁡
(
−
x
)
)

/

2
)

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

cosh(Z)

R
e
a
l
=
cos
⁡
(
y
)
(
(
exp
⁡
(
x
)
+
exp
⁡
(
−
x
)
)

/

2
)

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

I
m
a
g
=
sin
⁡
(
y
)
(
(
exp
⁡
(
x
)
−
exp
⁡
(
−
x
)
)

/

2
)

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

= Images =
See : commons:Category:Trigonometric maps

= Videos =
youtube : Spirals and Slarips by Gary Welz

Paul Bourke : sinjulia fractal