Journal of Formalized Mathematics
Volume 14, 2002
University of Bialystok
Copyright (c) 2002 Association of Mizar Users

Trigonometric Functions on Complex Space


Takashi Mitsuishi
Miyagi University
Noboru Endou
Gifu National College of Technology
Keiji Ohkubo
Shinshu University, Nagano

Summary.

This article describes definitions of sine, cosine, hyperbolic sine and hyperbolic cosine. Some of their basic properties are discussed.

MML Identifier: SIN_COS3

The terminology and notation used in this paper have been introduced in the following articles [11] [9] [5] [12] [1] [10] [4] [3] [2] [6] [8] [13] [7]

Contents (PDF format)

  1. Definitions of Trigonometric Functions
  2. Properties of Trigonometric Functions on Complex Space

Bibliography

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Journal of Formalized Mathematics, 1, 1989.
[2] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[3] Czeslaw Bylinski. The complex numbers. Journal of Formalized Mathematics, 2, 1990.
[4] Library Committee. Introduction to arithmetic. Journal of Formalized Mathematics, Addenda, 2003.
[5] Krzysztof Hryniewiecki. Basic properties of real numbers. Journal of Formalized Mathematics, 1, 1989.
[6] Jaroslaw Kotowicz. Real sequences and basic operations on them. Journal of Formalized Mathematics, 1, 1989.
[7] Takashi Mitsuishi and Yuguang Yang. Properties of the trigonometric function. Journal of Formalized Mathematics, 11, 1999.
[8] Yasunari Shidama and Artur Kornilowicz. Convergence and the limit of complex sequences. Series. Journal of Formalized Mathematics, 9, 1997.
[9] Andrzej Trybulec. Subsets of real numbers. Journal of Formalized Mathematics, Addenda, 2003.
[10] Wojciech A. Trybulec. Pigeon hole principle. Journal of Formalized Mathematics, 2, 1990.
[11] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[12] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[13] Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Journal of Formalized Mathematics, 10, 1998.

Received October 10, 2002


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