@MISC{SIN_COS.MIZ,
  AUTHOR = {Yang, Yuguang and Shidama, Yasunari},
  TITLE = {Trigonometric Functions and Existence of Circle Ratio},
  SECTION1 = {Some Definitions and Properties of Complex Sequence},
  SECTION2 = {Definition of Exponential Function on Complex},
  SECTION3 = {Definition of Sinus, Cosine, and Exponential Function on ${\Bbb R}$},
  SECTION4 = {Differential of Sinus, Cosine, and Exponential Function},
  SECTION5 = {Existence of Circle Ratio},
  SECTION6 = {Formulas of Sinus, Cosine},
  DAY = {22},
  MONTH = {October},
  YEAR = {1998},
  ADDRESS1 = {Shinshu University\\Nagano},
  ADDRESS2 = {Shinshu University\\Nagano},
  SUMMARY = {In this article, we defined {\em sinus} and {\em cosine} as the real part 
and the imaginary part
of the exponential function on complex, and also give their series expression.
Then we proved the differentiablity of {\em sinus}, {\em cosine} 
and the exponential function
of real. Finally, we showed the existence of the circle ratio, and some formulas
 of {\em sinus}, {\em cosine}.}}

