What does the cosine function represent in relation to the sides of a triangle?

The cosine function represents the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. The adjacent side is the side that is next to the angle in question (other than the hypotenuse), while the hypotenuse is the longest side of the triangle, opposite the right angle.

When you analyze a right triangle and focus on one of the non-right angles, the cosine function provides a way to relate the lengths of the sides of the triangle to the angle's measure. This relationship is fundamental in trigonometry and is key to solving problems involving right triangles, especially in applications such as physics, engineering, and various fields that utilize geometric principles.

In contrast, the other ratios represented by the choices are associated with different trigonometric functions: the sine function relates to the opposite side and hypotenuse, and the tangent function relates to the opposite side and adjacent side. Therefore, identifying the cosine function correctly as adjacent over hypotenuse is critical for understanding and applying these relationships effectively in real-world scenarios.