| Title |
Algebrinės sinusų ir kosinusų bei jų argumentų reikšmės / |
| Translation of Title |
Algebraic values of sines and cosines and their arguments. |
| Authors |
Mazėtis, Edmundas ; Melničenko, Grigorijus |
| DOI |
10.15388/LMR.2020.22717 |
| Full Text |
|
| Is Part of |
Lietuvos matematikos rinkinys. Ser. B.. Vilnius : Vilniaus universiteto leidykla. 2020, t. 61, p. 21-28.. ISSN 0132-2818. eISSN 2335-898X |
| Keywords [eng] |
trigonometric functionssinα,cosα,tgαirctgα ; rational numbers ; algebraic numbers ; transcendental numbers ; Lindemann–Weierstrass theorem |
| Abstract [eng] |
The article introduces the reader to some amazing properties of trigonometric functions. It turns out that if the values of the arguments of the functions sin x, cos x, tg x and ctg x, expressed in radians, are algebraic numbers, then the values of these functions are transcendental numbers. Hence, it follows that the values of all angles of the pseudo-Heronian triangle, including the values of all angles of the Pythagoras or Heron triangle, expressed in radians, are transcendental numbers. If the arguments of functions sin x and cos x, expressed in radians, are equal to x = r 2 \pi, where r are rational numbers, then the values of the functions are algebraic numbers. It should be noted that in this case the argument x = r 2\pi is transcendental and, if expressed in degrees, becomes a rational. |
| Published |
Vilnius : Vilniaus universiteto leidykla |
| Type |
Journal article |
| Language |
Lithuanian |
| Publication date |
2020 |
| CC license |
|
