MathsPrime

📘 Aide — Trigonométrie

Relation fondamentale :
\(\cos^2(x) + \sin^2(x) = 1\)

Valeurs remarquables :

\(x\)	\(0\)	\(\dfrac{\pi}{6}\)	\(\dfrac{\pi}{4}\)	\(\dfrac{\pi}{3}\)	\(\dfrac{\pi}{2}\)	\(\pi\)
\(\cos(x)\)	\(1\)	\(\dfrac{\sqrt{3}}{2}\)	\(\dfrac{\sqrt{2}}{2}\)	\(\dfrac{1}{2}\)	\(0\)	\(-1\)
\(\sin(x)\)	\(0\)	\(\dfrac{1}{2}\)	\(\dfrac{\sqrt{2}}{2}\)	\(\dfrac{\sqrt{3}}{2}\)	\(1\)	\(0\)

Signes par quadrant :
\([0, \pi/2]\) : cos ≥ 0, sin ≥ 0  |  \([\pi/2, \pi]\) : cos ≤ 0, sin ≥ 0
\([\pi, 3\pi/2]\) : cos ≤ 0, sin ≤ 0  |  \([3\pi/2, 2\pi]\) : cos ≥ 0, sin ≤ 0

Symétries :
\(\sin(\pi - x) = \sin(x)\)  |  \(\cos(\pi - x) = -\cos(x)\)
\(\sin(-x) = -\sin(x)\)  |  \(\cos(-x) = \cos(x)\)

Périodicité :
\(\sin(x + 2k\pi) = \sin(x)\)  |  \(\cos(x + 2k\pi) = \cos(x)\)

Leçon complète