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).
If a function f(x) has a period = t, then the function n*f(kx) has a period = t/k. We know that the function f(x) = sin(x) has a period = 2*pi. Thus the function f(x) = 2sin(5x) will have a period = (2/5)*pi. The maximum value of sin(5x) is 1 and the mean value is 0. Thus the amplitude of y=2sin(5x) is equal to 2.