Question
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Evaluate the following trigonometric function at the quadrantal angle, or state that the expression is undefined. \( \cos \pi \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The value of \( \cos \pi \) is B. \( \cos \pi \) is undefined.

Ask by Spencer Adkins. in the United States
Dec 03,2024

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Answer

A. The value of \( \cos \pi \) is \(-1\).

Solution

To evaluate \( \cos \pi \), we can refer to the unit circle. The angle \( \pi \) radians corresponds to 180 degrees, which is located on the negative x-axis. The coordinates of the point on the unit circle at this angle are \((-1, 0)\). The cosine of an angle is defined as the x-coordinate of the corresponding point on the unit circle. Thus, we have: \[ \cos \pi = -1 \] So the correct choice is: A. The value of \( \cos \pi \) is \(-1\).

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A. The value of \( \cos \pi \) is -1. In the unit circle, \( \pi \) radians corresponds to the angle of 180 degrees, which lies on the negative x-axis. Here, the coordinates are (-1, 0), and thus the cosine value, which represents the x-coordinate, is -1.

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