For 10 points, name this trigonometric function computed as the opposite leg over the hypotenuse.
The values returned by this function are the subject of Niven's theorem, and as a function of z, this function can be defined complexly as e to the i z minus e to the negative i z all over two i. This function's Maclaurin series begins with x minus x-cubed over three factorial plus x to the fifth over five factorial. The ratio between this function of a given angle in a triangle and the side opposite that angle is constant according to the "law of" this function, and the derivative of this function is cosine. For 10 points, name this trigonometric function computed as the opposite leg over the hypotenuse.
The values returned by this function are the subject of Niven's theorem, and as a function of z, this function can be defined complexly as e to the i z minus e to the negative
Sine