Question

find the exact value of the expression

$\tan (330°)$

Short answer

$\tan (330°)=-\frac{1}{\sqrt{3}}$

Step-by-step solution

Step 1. Rewriting the expression  

We know that

$$\begin{gathered} \tan (2\mathrm{\pi }-\mathrm{x})=-\tan \left(\mathrm{x}\right) \\ So\tan (330°)=\tan (2\mathrm{\pi }-30)=-\tan \left(30\right) \end{gathered}$$

Step 2. Calculations 

Now we get the expression as$$\begin{gathered} \tan (330°)=-\tan (30°) \\ So-\tan (30°)=-\frac{1}{\sqrt{3}} \end{gathered}$$