find the exact value of \\( \\sec ( - \\pi ) \\). do not use a calculator.\n\n\\( \\sec ( - \\pi ) = \\)…

Explanation:

Step1: Use the property of secant function

The secant function is an even function, so (\sec(-x)=\sec(x)). Then (\sec(-\pi)=\sec(\pi)).

Step2: Use the reciprocal identity

Recall that (\sec(x)=\frac{1}{\cos(x)}). So (\sec(\pi)=\frac{1}{\cos(\pi)}).

Step3: Find the value of (\cos(\pi))

We know that on the unit - circle, for the angle (x = \pi) (the point ((- 1,0)) on the unit - circle), (\cos(\pi)=-1).

Step4: Calculate (\sec(\pi))

Substitute (\cos(\pi)=-1) into (\sec(\pi)=\frac{1}{\cos(\pi)}), we get (\sec(\pi)=\frac{1}{-1}=-1).

Answer:

(-1)