Some Facts about Trigonometry and Euclidean Geometry

Roland Coghetto

Formalized Mathematics, Tome 22 (2014), p. 313-319 / Harvested from The Polish Digital Mathematics Library

Résumé

We calculate the values of the trigonometric functions for angles: [XXX] , by [16]. After defining some trigonometric identities, we demonstrate conventional trigonometric formulas in the triangle, and the geometric property, by [14], of the triangle inscribed in a semicircle, by the proposition 3.31 in [15]. Then we define the diameter of the circumscribed circle of a triangle using the definition of the area of a triangle and prove some identities of a triangle [9]. We conclude by indicating that the diameter of a circle is twice the length of the radius

Détail

Publié le : 2014-01-01

Zbl 1316.51006

EUDML-ID : urn:eudml:doc:270835

Bibliographie

[1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.

[2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.

[3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.

[4] Czesław Bylinski. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.

[5] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.

[6] Czesław Bylinski. Introduction to real linear topological spaces. Formalized Mathematics, 13(1):99-107, 2005.

[7] Czesław Bylinski. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.

[8] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.

[9] H.S.M. Coxeter and S.L. Greitzer. Geometry Revisited. The Mathematical Association of America (Inc.), 1967. | Zbl 0166.16402

[10] Agata Darmochwał. Compact spaces. Formalized Mathematics, 1(2):383-386, 1990.

[11] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.

[12] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.

[13] Alicia de la Cruz. Totally bounded metric spaces. Formalized Mathematics, 2(4):559-562, 1991.

[14] Nikolai Vladimirovich Efimov. G´eom´etrie sup´erieure. Mir, 1981.

[15] Richard Fitzpatrick. Euclid’s Elements. Lulu.com, 2007.

[16] Robin Hartshorne. Geometry: Euclid and beyond. Springer, 2000.

[17] Stanisława Kanas, Adam Lecko, and Mariusz Startek. Metric spaces. Formalized Mathematics, 1(3):607-610, 1990.

[18] Artur Korniłowicz and Yasunari Shidama. Inverse trigonometric functions arcsin and arccos. Formalized Mathematics, 13(1):73-79, 2005. | Zbl 1276.26026

[19] Akihiro Kubo and Yatsuka Nakamura. Angle and triangle in Euclidean topological space. Formalized Mathematics, 11(3):281-287, 2003.

[20] Robert Milewski. Trigonometric form of complex numbers. Formalized Mathematics, 9 (3):455-460, 2001.

[21] Yatsuka Nakamura. General Fashoda meet theorem for unit circle and square. Formalized Mathematics, 11(3):213-224, 2003.

[22] Yatsuka Nakamura and Czesław Bylinski. Extremal properties of vertices on special polygons. Part I. Formalized Mathematics, 5(1):97-102, 1996.

[23] Chanapat Pacharapokin, Kanchun, and Hiroshi Yamazaki. Formulas and identities of trigonometric functions. Formalized Mathematics, 12(2):139-141, 2004.

[24] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.

[25] Marco Riccardi. Heron’s formula and Ptolemy’s theorem. Formalized Mathematics, 16 (2):97-101, 2008. doi:10.2478/v10037-008-0014-2.[Crossref]

[26] Andrzej Trybulec and Czesław Bylinski. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.

[27] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

[28] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.

[29] Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998.