This gives the meaning of the terms as generally understood in the middle of the 18th century. Robert Hooper's Physician's Vade-Mecum, published in 1812 has been used as a source of terms in the early 19th century; many of the terms mentioned are still in common use.
In either case, the value at x = 0 is defined to be the limiting value sinc(0) = 1. The normalization causes the definite integral of the function over the real numbers to equal 1 (whereas the same integral of the unnormalized sinc function has a value of Ï).
You can see this clearly if you consider the unit circle, where sin(t) = y, cos(t) = x, and the hypotenuse is 1. sin(t) = sin(t) cos(t) = cos(t) tan(t) = tan(t) Notice in particular that sine and tangent are odd functions, while cosine is an even function. Angle-Sum and -Difference Identities.