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).
tan(x y) = (tan x tan y) / (1 tan x tan y). sin(2x) = 2 sin x cos x. cos(2x) = cos ^2 (x) - sin ^2 (x) = 2 cos ^2 (x) - 1 = 1 - 2 sin ^2 (x). tan(2x) = 2 tan(x) / (1 - tan ^2 (x)). sin ^2 (x) = 1/2 - 1/2 cos(2x). cos ^2 (x) = 1/2 + 1/2 cos(2x). sin x-sin y = 2 sin((x-y)/2) cos((x + y)/2). cos x-cos y = -2 sin((x-y)/2) sin((x + y)/2).