Journal of Formalized Mathematics
Volume 10, 1998
University of Bialystok
Copyright (c) 1998 Association of Mizar Users

Trigonometric Functions and Existence of Circle Ratio


Yuguang Yang
Shinshu University, Nagano
Yasunari Shidama
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}.

MML Identifier: SIN_COS

The terminology and notation used in this paper have been introduced in the following articles [23] [26] [3] [24] [7] [8] [4] [19] [5] [11] [9] [20] [27] [18] [16] [2] [13] [6] [25] [17] [10] [21] [15] [12] [1] [14] [22]

Contents (PDF format)

  1. Some Definitions and Properties of Complex Sequence
  2. Definition of Exponential Function on Complex
  3. Definition of Sinus, Cosine, and Exponential Function on ${\Bbb R}$
  4. Differential of Sinus, Cosine, and Exponential Function
  5. Existence of Circle Ratio
  6. Formulas of Sinus, Cosine

Bibliography

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Received October 22, 1998


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