evaluate. write your answer in simplified, rationalized form. do not round.\n\n\\( \\tan ( - \\pi ) = \\)\n

Explanation:

Step1: Use the property of tangent function

The tangent function is odd, i.e., $\tan(-x)=-\tan(x)$. So, $\tan(-\pi)=-\tan(\pi)$.

Step2: Evaluate $\tan(\pi)$

We know that $\tan(x)=\frac{\sin(x)}{\cos(x)}$, and for $x = \pi$, $\sin(\pi)=0$ and $\cos(\pi)=- 1$. Then $\tan(\pi)=\frac{\sin(\pi)}{\cos(\pi)}=\frac{0}{-1}=0$.

Step3: Calculate the final value

Since $\tan(-\pi)=-\tan(\pi)$ and $\tan(\pi) = 0$, then $\tan(-\pi)=-0 = 0$.

Answer:

$0$