Problem 43 - Algebra and Trigonometry Real Mathematics, Real People

Question

Evaluate the trigonometric function of the quadrant angle, if possible. $$\sec \pi$$

Step-by-Step Solution

Answer

The value of \(\sec(\pi)\) is -1.

Step 1: Find the Cosine

To evaluate the secant, it's useful to first evaluate the cosine since the secant is the reciprocal of the cosine. We know that the cosine of \(\pi\) radians is -1. This is a well-known and important property in trigonometry.

Step 2: Find the Reciprocal

Next, the secant of \(\pi\) radians is the reciprocal of the cosine of \(\pi\) radians. The reciprocal of -1 is -1.

Step 3: Write Down the Final Answer

Having calculated the secant of \(\pi\) radians as the reciprocal of the cosine of \(\pi\) radians, it's clear that \(\sec(\pi) = -1.\)