When this function is divided by its input, a new function results that acts as the ideal reconstruction filter. That filter exhibits the Gibbs phenomenon, and this function i
When this function is divided by its input, a new function results that acts as the ideal reconstruction filter. That filter exhibits the Gibbs phenomenon, and this function is used in Fourier series representations of odd functions.  In Euler's formula, this function represents the imaginary part and as such is multiplied by i. The Taylor series for this function consist of alternating terms of the form X to N where N is odd, divided by N factorial. Its derivative is cosine, a function that is this function shifted by 90 degrees.  For 10 points, name this trigonometric function that for an angle is equal to the length of the opposite side divided by the hypotenuse.
When this function is divided by its input, a new function results that acts as the ideal reconstruction filter.
sine