Question

Use the unit circle to evaluate the followingHow do I solve this ?

Answer 1

So we want to evaluate:

`\tan ((2\pi)/(3))`

For this, we might convert 2pi/3 to degrees.

This, is to make the graph more understandable.

Remember that:

`\pi=180`

So we could make the following ratio:

`\begin{gathered} \pi=180 \\ (2\pi)/(3)=x \end{gathered}`

Solving for x:

`\begin{gathered} x=((2\pi)/(3)\cdot180)/(\pi) \\ \\ x=(120\pi)/(\pi)=120 \end{gathered}`

Therefore, x=120°. Now, we could graph:

So,

`\tan (120)=(\sin120)/(\cos120)=(\sin 60)/(-\cos 60)=\frac{\frac{\sqrt[]{3}}{2}}{-(1)/(2)}=-\sqrt[]{3}`