Which function can be defined as the ratio of the opposite side to the adjacent side in a right triangle?

The function that is defined as the ratio of the opposite side to the adjacent side in a right triangle is tangent. In trigonometry, tangent is specifically used to relate these two sides in regard to an angle within the triangle. The formula for tangent is expressed as:

[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}

]

This means that if you know the lengths of the opposite side and the adjacent side of a right triangle, you can determine the tangent of the angle formed by these sides. This relationship is fundamental in trigonometry and is widely used in various applications, such as solving right triangles, analyzing angles of elevation and depression, and in modeling periodic phenomena.

Other trigonometric functions like sine and cosine refer to different ratios; sine relates the opposite side to the hypotenuse, while cosine relates the adjacent side to the hypotenuse. Cotangent is the reciprocal of tangent, calculated as the ratio of the adjacent side to the opposite side. Understanding these definitions is key to applying trigonometric functions correctly in solving problems involving right triangles.