Problem

Find the exact value of $\sec 180^{\circ}$ in simplest form with a rational denominator.

Answer

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Answer

Final Answer: The exact value of \(\sec 180^\circ\) in simplest form with a rational denominator is \(\boxed{-1}\).

Steps

Step 1 ：The secant function is the reciprocal of the cosine function. So, to find the secant of an angle, we first need to find the cosine of that angle.

Step 2 ：The cosine of 180 degrees is -1.

Step 3 ：Therefore, the secant of 180 degrees is the reciprocal of -1, which is -1.

Step 4 ：Final Answer: The exact value of \(\sec 180^\circ\) in simplest form with a rational denominator is \(\boxed{-1}\).

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