How is the cosine function of a negative angle expressed?

The cosine function, like many other trigonometric functions, exhibits specific properties related to the angle's sign. In the case of cosine, it is an even function. This means that for any angle ( x ), the cosine of the negative angle is equal to the cosine of the positive angle. Mathematically, this property is expressed as ( \cos(-x) = \cos(x) ).

This even nature of the cosine function can be understood through the unit circle or the symmetry it shares in the coordinate plane. When we reflect a point across the y-axis, the x-coordinate of the point (which determines the cosine value) remains the same, while the y-coordinate (which determines the sine value) changes sign. Thus, while the cosine value stays unchanged for positive and negative angles, the sine value reflects a change.

Other responses do not apply in this case. The second choice suggests that the cosine of a negative angle is the negative of the cosine of the positive angle, which contradicts the even property of cosine. Choices involving sine, including the third and fourth responses, misinterpret the behaviors of these functions since sine functions are odd and changing signs occurs with the negative angle.

Therefore, the correct expression for ( \cos