for the function f(x) = tan x, evaluate f(5π/6).

Explanation:

Step1: Recall tangent formula

$\tan x=\frac{\sin x}{\cos x}$

Step2: Find $\sin(\frac{5\pi}{6})$ and $\cos(\frac{5\pi}{6})$

$\sin(\frac{5\pi}{6})=\frac{1}{2}$, $\cos(\frac{5\pi}{6})=-\frac{\sqrt{3}}{2}$

Step3: Calculate $\tan(\frac{5\pi}{6})$

$\tan(\frac{5\pi}{6})=\frac{\sin(\frac{5\pi}{6})}{\cos(\frac{5\pi}{6})}=\frac{\frac{1}{2}}{-\frac{\sqrt{3}}{2}}=-\frac{1}{\sqrt{3}}=-\frac{\sqrt{3}}{3}$

Answer:

$-\frac{\sqrt{3}}{3}$