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 your calculator is on the degree mode, it is computing the sine, cosine or tangent of an angle the size of the number you put in. Note that the sine of $390$ will be the same as that of $30$ since adding one full revolution doesn't change the angle. However, if you want to know how a calculator finds values for the functions numerically, you might want to have a look at Taylor Series.