For 10 points, name this trigonometric function, which in a right triangle is equal to the opposite over the hypotenuse.
This function is the imaginary part of Euler's formula, and its hyperbolic version is equal to one-half of the quantity "e to the x minus e to the negative x." This function's namesake law states that the ratio of this function of one angle to the length of the side opposite that angle is equal for all three angles, and its multiplicative inverse is the cosecant function. For 10 points, name this trigonometric function, which in a right triangle is equal to the opposite over the hypotenuse.
This function is the imaginary part of Euler's formula, and its hyperbolic version is equal to one-half of the quantity "e to the x minus e to the negative x." This function's namesake law states that the ratio of this function of one angle to the length of the side opposite that angle is equal for all three angles, and its multiplicative inverse is the cosecant function.
{sine}