In the present book, a new form of trigonometric relations have been presented and discussed on adopting functions named as Nbic functions, created as the combination of circular and hyperbolic functions of several varieties by separating the real and imaginary parts of the product of complex circular and complex hyperbolic functions of simple or higher orders. Though the variations of the Nbic functions are limitless, the scope of the present book covers only Single, Double and Triple Nbic functions. Single Nbic functions, being the simplest of all the varieties, already are in extensive use in the solution of differential equations of fourth and eighth order, as the combinations of, sin-cosh, cos-sinh etc., which are often encountered in structural mechanics and elasticity problems.