I'm studying specular reflection in dance flies, and I'm stuck on trigonometry. Imagine a circle with a right triangle inscribed. The hypotenuse is the radius of the circle, and one vertex rests on the center of the circle. What is the trigonometric function that describes the relationship between the angle of that vertex and the length of the opposite side (i.e., the side adjacent to the hypotenuse)? To clarify: When the vertex angle is very near 90 degrees, the length of the opposite side is very near the radius of the circle, and when the vertex angle is very near zero degrees, the adjacent side is very near zero. But what is the function that describes everything in between?