//by Richard Russell, April 2018//

BBC 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 bb4w>
      DEF FNsinh(x) = (EXP(x) - EXP(-x)) / 2
      DEF FNcosh(x) = (EXP(x) + EXP(-x)) / 2
      DEF FNtanh(x) = (EXP(x) - EXP(-x)) / (EXP(x) + EXP(-x))
      DEF FNcoth(x) = (EXP(x) + EXP(-x)) / (EXP(x) - EXP(-x))
      DEF FNsech(x) = 2 / (EXP(x) + EXP(-x))
      DEF FNcsch(x) = 2 / (EXP(x) - EXP(-x))
</code>