Which trigonometric function equals the ratio of the adjacent side to the hypotenuse?

The correct answer is cosine, which is defined as the ratio of the length of the adjacent side to the hypotenuse in a right triangle. In a right-angled triangle, if you consider an angle, the adjacent side is the side next to the angle that is not the hypotenuse, which is the longest side of the triangle. The formula for cosine in relation to a right triangle can be expressed as:

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

This clearly demonstrates that cosine is specifically the ratio that relates the adjacent side to the hypotenuse for any given angle (\theta).

The sine function, on the other hand, relates the opposite side to the hypotenuse, making it unsuitable for this specific ratio. Tangent, meanwhile, represents the ratio of the opposite side to the adjacent side, and cosecant is the reciprocal of the sine, which connects the hypotenuse to the opposite side rather than the adjacent side. Thus, cosine is the only function among the choices that accurately matches the required ratio.