In a triangle, for any angle the value of this function divided by the length of the opposite side is a constant, a result known as this function's namesake law.
The hyperbolic version of this function is "e to the x, minus e to the negative x, all over two." Taking a side length of a triangle and dividing by this function applied to the opposite angle gives the diameter of the circle that circumscribes the triangle. In a triangle, for any angle the value of this function divided by the length of the opposite side is a constant, a result known as this function's namesake law. For 10 points, name this trigonometric function which is the reciprocal of the cosecant, and which is defined for an angle in a right triangle as opposite over hypotenuse.
The hyperbolic version of this function is "e to the x, minus e to the negative x, all over two."
{sine}