So we want to evaluate:
[tex]\tan (\frac{2\pi}{3})[/tex]
For this, we might convert 2pi/3 to degrees.
This, is to make the graph more understandable.
Remember that:
[tex]\pi=180[/tex]
So we could make the following ratio:
[tex]\begin{gathered} \pi=180 \\ \frac{2\pi}{3}=x \end{gathered}[/tex]
Solving for x:
[tex]\begin{gathered} x=\frac{\frac{2\pi}{3}\cdot180}{\pi} \\ \\ x=\frac{120\pi}{\pi}=120 \end{gathered}[/tex]
Therefore, x=120°. Now, we could graph:
So,
[tex]\tan (120)=\frac{\sin120}{\cos120}=\frac{\sin 60}{-\cos 60}=\frac{\frac{\sqrt[]{3}}{2}}{-\frac{1}{2}}=-\sqrt[]{3}[/tex]
