What is the cosine function in trigonometry represented as?

The cosine function in trigonometry is defined as the ratio of the length of the side adjacent to an angle to the length of the hypotenuse in a right triangle. This definition applies specifically to a right triangle, where the hypotenuse is the longest side, opposite the right angle, and the adjacent side is one of the other two sides, pertaining to the angle in question.

In this context, the cosine of an angle (often denoted as cos(θ)) can be expressed mathematically as:

cos(θ) = length of the adjacent side / length of the hypotenuse.

This fundamental relationship is crucial for solving a wide range of problems in trigonometry, from calculating unknown side lengths or angles in right triangles to working with periodic functions in higher mathematics. Understanding this ratio helps students navigate through various applications in geometry, physics, and engineering.