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

find the exact value of \\( \\sec ( - \\pi ) \\). do not use a calculator.\n\\( \\sec ( - \\pi ) = \\square \\)\n(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

find the exact value of \\( \\sec ( - \\pi ) \\). do not use a calculator.\n\\( \\sec ( - \\pi ) = \\square \\)\n(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

Answer

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: Recall the definition of secant function

We know that (\sec(x)=\frac{1}{\cos(x)}). For (x = \pi), (\cos(\pi)=- 1).

Step3: Calculate the value of (\sec(\pi))

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

Answer:

(-1)