A distinctive Sumudu treatment of trigonometric functions

The Sumudu transform integral equation is solved by continuous integration by parts, to obtain its definition for trigonometric functions. The transform variable, uu, is included as a factor in the argument of f(t)f(t), and summing the integrated coefficients evaluated at zero yields the image of trigonometric functions. The obtained result is inverted to show the expansion of trigonometric functions as an infinite series. Maple graphs, tables of extended Sumudu properties, and infinite series expansions of trigonometric functions Sumudi images are given.