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).
The reason is that the value of sine for the angle of the triangle does not uniquely determine this angle. For example, if sin Î² = 0.5, the angle Î² can equal either 30Â° or 150Â°. Using the law of cosines avoids this problem: within the interval from 0Â° to 180Â° the cosine value unambiguously determines its angle.