# Hyperbolic functions

These are of occasional use- as are the inverses of trig functions.

In nature, represent the shape of a rope hung from to places- the 'catenary'.

## Code

```    nomainwin

WindowWidth  =550
WindowHeight =550

open "Demo of hyperbolic functions" for graphics_nsb as #gw

#gw "trapclose quit"
#gw "goto 255 0 ; down ; goto 255 550 ; up"
#gw "goto 0 255 ; down ; goto 550 255"

for x =-5 to 5 step 0.001
xScreen =255 +x *50
yScreen =255 -int( 50 *sinh( x))
#gw "color red ; set "; xScreen; " "; yScreen
yScreen =255 -int( 50 *cosh( x))
#gw "color green ; set "; xScreen; " "; yScreen
yScreen =255 -int( 50 *tanh( x))
#gw "color blue ; set "; xScreen; " "; yScreen
next x

#gw "getbmp scr 1 1 550 550"
bmpsave "scr", "hyperbolics.bmp"
wait

end

sub quit h\$
close #gw
end
end sub

function sinh( x)
sinh =( 1 -exp( 0 -2 *x)) /( 2 *exp( 0 -x))
end function

function cosh( x)
cosh =( 1 +exp( 0 -2 *x)) /( 2 * exp( 0 -x))
end function

function tanh( x)
tanh =( 1 -exp( 0 -2 *x)) /( 1 + exp( 0 -2 *x))
end function

```