Algebraic relations between sine and cosine values
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909215496339456 |
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| author | Adamczewski, B. Delaygue, É. |
| author_facet | Adamczewski, B. Delaygue, É. |
| contents | The aim of this note is to show that any algebraic relation over $\overline{\mathbb{Q}}$ between the values of the trigonometric functions sine and cosine at algebraic points can be derived from the Pythagorean identity and the angle addition formulas. This result is obtained as a consequence of the Lindemann-Weierstrass theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01296 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algebraic relations between sine and cosine values Adamczewski, B. Delaygue, É. Number Theory 11J81 (Primary), 11J85 (Secondary) The aim of this note is to show that any algebraic relation over $\overline{\mathbb{Q}}$ between the values of the trigonometric functions sine and cosine at algebraic points can be derived from the Pythagorean identity and the angle addition formulas. This result is obtained as a consequence of the Lindemann-Weierstrass theorem. |
| title | Algebraic relations between sine and cosine values |
| topic | Number Theory 11J81 (Primary), 11J85 (Secondary) |
| url | https://arxiv.org/abs/2406.01296 |