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.
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}