Calcular el valor de les funcions trigonomètriques (sinus, cosinus i tangent) de $$x=\dfrac{5\pi}{6}$$ rad.
Veure desenvolupament i solució
Desenvolupament:
L'angle $$\dfrac{5\pi}{6}$$ és un angle del segon quadrant, és a dir, $$\dfrac{\pi}{2} < \dfrac{5\pi}{6} < \pi$$, per tant tenim: $$$\sin(x)=\sin(\dfrac{5\pi}{6})=\sin(\pi-\dfrac{5\pi}{6})=\sin(\dfrac{\pi}{6})=\dfrac{1}{2}$$$
$$$\cos(x)=\cos(\dfrac{5\pi}{6})=-\cos(\pi-\dfrac{5\pi}{6})=-\cos(\dfrac{\pi}{6})=-\dfrac{\sqrt{3}}{2}$$$
$$$\tan(x)=\tan(\dfrac{5\pi}{6})=-\tan(\pi-\dfrac{5\pi}{6})=-\tan(\dfrac{\pi}{6})=-\dfrac{\sqrt{3}}{3}$$$
Solució:
$$\sin(x)=\dfrac{1}{2}$$
$$\cos(x)=-\dfrac{\sqrt{3}}{2}$$
$$\tan(x)=-\dfrac{\sqrt{3}}{3}$$