Half Angle Formulae

A set of formulae expressing trigonometric functions of an angle x in terms of an angle 2x,

Personally I think it is a lot easier to simply use the Double Angle Formulae in reverse, as opposed to remembering a new set of formulae which are ultimately redundant. However, for those who like pain, here we are:

    sin2(½Θ) = ½(1 - cos(Θ))

    cos2(½Θ) = ½(1 + cos(Θ))

                sin(Θ)
    tan(½Θ) = ----------
              1 + cos(Θ)

              1 - cos(Θ)
            = ----------
                sin(Θ)

               tan(Θ)sin(Θ)
            = --------------
              tan(Θ) + sin(Θ)

Through the use of Osborne's rule we can arrive at the corresponding set of formulae for hyperbolic functions,

    sinh2(½Θ) = ½(cosh(Θ) - 1)

    cosh2(½Θ) = ½(cosh(Θ) + 1)

                  sinh(Θ)
    tanh(½Θ) = ------------
               cosh(Θ) + 1

               cosh(Θ) - 1
             = ------------
                  sinh(Θ)

To reverse the process you may use the Double Angle Formulae.