Mathématiques
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Rappels de Trigonométrie pour les Complexes
Les Nombres Complexes
Outils de Trigonométrie
Valeurs remarquables
| $x$ | $0$ | $\frac{\pi}{6}$ | $\frac{\pi}{4}$ | $\frac{\pi}{3}$ | $$\sin(a \pm b) = \sin a \cos b \pm \cos a \sin b$$0 | $$\sin(a \pm b) = \sin a \cos b \pm \cos a \sin b$$1 |
|---|---|---|---|---|---|---|
| $$\sin(a \pm b) = \sin a \cos b \pm \cos a \sin b$$2 | $$\sin(a \pm b) = \sin a \cos b \pm \cos a \sin b$$3 | $$\sin(a \pm b) = \sin a \cos b \pm \cos a \sin b$$4 | $$\sin(a \pm b) = \sin a \cos b \pm \cos a \sin b$$5 | $$\sin(a \pm b) = \sin a \cos b \pm \cos a \sin b$$6 | $$\sin(a \pm b) = \sin a \cos b \pm \cos a \sin b$$7 | $$\sin(a \pm b) = \sin a \cos b \pm \cos a \sin b$$8 |
| $$\sin(a \pm b) = \sin a \cos b \pm \cos a \sin b$$9 | $$\cos(2a) = \cos^2 a - \sin^2 a = 2\cos^2 a - 1 = 1 - 2\sin^2 a$$0 | $$\cos(2a) = \cos^2 a - \sin^2 a = 2\cos^2 a - 1 = 1 - 2\sin^2 a$$1 | $$\cos(2a) = \cos^2 a - \sin^2 a = 2\cos^2 a - 1 = 1 - 2\sin^2 a$$2 | $$\cos(2a) = \cos^2 a - \sin^2 a = 2\cos^2 a - 1 = 1 - 2\sin^2 a$$3 | $$\cos(2a) = \cos^2 a - \sin^2 a = 2\cos^2 a - 1 = 1 - 2\sin^2 a$$4 | $$\cos(2a) = \cos^2 a - \sin^2 a = 2\cos^2 a - 1 = 1 - 2\sin^2 a$$5 |
| $$\cos(2a) = \cos^2 a - \sin^2 a = 2\cos^2 a - 1 = 1 - 2\sin^2 a$$6 | $$\cos(2a) = \cos^2 a - \sin^2 a = 2\cos^2 a - 1 = 1 - 2\sin^2 a$$7 | $$\cos(2a) = \cos^2 a - \sin^2 a = 2\cos^2 a - 1 = 1 - 2\sin^2 a$$8 | $$\cos(2a) = \cos^2 a - \sin^2 a = 2\cos^2 a - 1 = 1 - 2\sin^2 a$$9 | $$\sin(2a) = 2\sin a \cos a$$0 | — | $$\sin(2a) = 2\sin a \cos a$$1 |
Formules d'addition
$$\cos(a \pm b) = \cos a \cos b \mp \sin a \sin b$$
$$\sin(a \pm b) = \sin a \cos b \pm \cos a \sin b$$
Formules de duplication
$$\cos(2a) = \cos^2 a - \sin^2 a = 2\cos^2 a - 1 = 1 - 2\sin^2 a$$
$$\sin(2a) = 2\sin a \cos a$$
Formule fondamentale
$$\cos^2(x) + \sin^2(x) = 1$$
Ces formules sont essentielles pour la détermination des formes trigonométrique et exponentielle des nombres complexes.