evaluate. write your answer in simplified, rationalized form. do not round. tan 60° =

Explanation:

Step1: Recall tangent - sine/cosine relation

$\tan\theta=\frac{\sin\theta}{\cos\theta}$, so $\tan60^{\circ}=\frac{\sin60^{\circ}}{\cos60^{\circ}}$.

Step2: Know sine and cosine values

We know that $\sin60^{\circ}=\frac{\sqrt{3}}{2}$ and $\cos60^{\circ}=\frac{1}{2}$.

Step3: Calculate the tangent value

$\tan60^{\circ}=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\sqrt{3}$.

Answer:

$\sqrt{3}$