If r is the hypotenuse in a right triangle, which expression represents cos?

In a right triangle, the cosine function is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. In this context, when considering a right triangle where ( r ) is the hypotenuse, ( x ) typically represents the length of the side that is adjacent to the angle being considered, and ( y ) represents the length of the opposite side.

The correct expression for cosine, therefore, is determined as follows:

• The hypotenuse ( r ) is the side opposite the right angle, serving as the reference for the trigonometric ratios.

• The adjacent side, which is the side next to the angle whose cosine we are calculating, is represented by ( x ).

Thus, the cosine of an angle in this triangle would be the ratio of the length of the adjacent side ( x ) to the length of the hypotenuse ( r ), leading to the expression ( \frac{x}{r} ). This accurately reflects the definition of the cosine function in trigonometry, confirming that the chosen expression represents cosine correctly.

For further clarity, the other expressions involve different ratios that do not conform to the definition of cosine, as they either involve the opposite side or