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

Explanation:

Step1: Recall the definition of secant

The secant function is defined as $\sec(x)=\frac{1}{\cos(x)}$. So, $\sec(\pi)=\frac{1}{\cos(\pi)}$.

Step2: Find the value of $\cos(\pi)$

We know that on the unit - circle, for $x = \pi$, the coordinates are $(- 1,0)$. And by the definition $\cos(x)=x$-coordinate of the point on the unit - circle corresponding to the angle $x$. So, $\cos(\pi)=-1$.

Step3: Calculate $\sec(\pi)$

Substitute $\cos(\pi)=-1$ into the formula $\sec(\pi)=\frac{1}{\cos(\pi)}$. We get $\sec(\pi)=\frac{1}{-1}$.

Answer:

$-1$