[<< 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


= See also =
Thorn Fractal, alternatively named the "Secant Sea"
Paul Bourke : sinjulia fractal