How is the cosine function represented in terms of a right triangle?

The cosine function is defined in the context of a right triangle as the ratio of the length of the side adjacent to the angle of interest to the length of the hypotenuse, which is the longest side of the triangle. This relationship can be summarized in the following way: if you have a right triangle with an angle θ, the adjacent side is the one that forms the angle with the hypotenuse, while the hypotenuse remains opposite to the right angle. The formula for cosine can thus be expressed as:

[ \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} ]

This definition is fundamental in trigonometry and applies to any angle in a right triangle, allowing the cosine function to be used in various applications, such as solving for missing sides or angles in geometric problems. Understanding this relationship is crucial for mastering more advanced concepts in trigonometry and related fields.