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Trigonometric ratios
Find the value of the trigonometric functions (sine, cosine and tangent) for $x=\dfrac{5\pi}{6}$ rad.
The angle $\dfrac{5\pi}{6}$ is an angle in the second quadrant, that is $\dfrac{\pi}{2} < \dfrac{5\pi}{6} < \pi$, therefore we have: $$\sin(x)=\sin(\dfrac{5\pi}{6})=\sin(\pi-\dfrac{5\pi}{6})=\sin(\dfrac{\pi}{6})=\dfrac{1}{2}$$
$$\cos(x)=\cos(\dfrac{5\pi}{6})=-\cos(\pi-\dfrac{5\pi}{6})=-\cos(\dfrac{\pi}{6})=-\dfrac{\sqrt{3}}{2}$$
$$\tan(x)=\tan(\dfrac{5\pi}{6})=-\tan(\pi-\dfrac{5\pi}{6})=-\tan(\dfrac{\pi}{6})=-\dfrac{\sqrt{3}}{3}$$
$$\sin(x)=\dfrac{1}{2}$$
$$\cos(x)=-\dfrac{\sqrt{3}}{2}$$
$$\tan(x)=-\dfrac{\sqrt{3}}{3}$$