//by Richard Russell, April 2018//

Liberty BASIC doesn't include the [[https://en.wikipedia.org/wiki/Hyperbolic_function|hyperbolic trig functions]] (**sinh**, **cosh**, **tanh** etc.) as a built-in feature, but they can easily be synthesised as user-defined functions as follows:

<code lb>
function sinh(x)
    sinh = (exp(x) - exp(-x)) / 2
end function

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

function tanh(x)
    tanh = (exp(x) - exp(-x)) / (exp(x) + exp(-x))
end function

function coth(x)
    coth = (exp(x) + exp(-x)) / (exp(x) - exp(-x))
end function

function sech(x)
    sech = 2 / (exp(x) + exp(-x))
end function

function csch(x)
    csch = 2 / (exp(x) - exp(-x))
end function
</code>