Functiones trigonometricae inversae
Functiones trigonometricae inversae sunt functiones inversae functionum trigonometricarum, quibus angulus ex rationibus trigonometricis anguli computantur. praefixo arc aut numero superiori −1 notantur. Secunda autem notatio potest ad ambiguitatem ducere, quia sin−1, exempli gratia, intellegi potest ut , hoc est csc A (cosecans).
| Nomen | Notatio | Definitio | Dominium definitionis x ad resultatum realem obtinendam | Imago valorium principalium usitatorum (radian) |
Imago valorium principalium usitatorum (gradus) |
|---|---|---|---|---|---|
| arcus sinus | y = arcsin x | x = sin y | −1 ≤ x ≤ 1 | −π/2 ≤ y ≤ π/2 | −90° ≤ y ≤ 90° |
| arcus cosinus | y = arccos x | x = cos y | −1 ≤ x ≤ 1 | 0 ≤ y ≤ π | 0° ≤ y ≤ 180° |
| arcus tangens | y = arctan x | x = tan y | omnes numeri reales | −π/2 < y < π/2 | −90° < y < 90° |
| arcus cotangens | y = arccot x | x = cot y | omnes numeri reales | 0 < y < π | 0° < y < 180° |
| arcus secans | y = arcsec x | x = sec y | x ≤ −1 or 1 ≤ x | 0 ≤ y < π/2 or π/2 < y ≤ π | 0° ≤ y < 90° or 90° < y ≤ 180° |
| arcus cosecans | y = arccsc x | x = csc y | x ≤ −1 or 1 ≤ x | −π/2 ≤ y < 0 or 0 < y ≤ π/2 | -90° ≤ y < 0° or 0° < y ≤ 90° |
Nexus externi
[recensere | fontem recensere]- "Inverse Trigonometric Functions" in lexico Wolfram Mathworld.