[math-fun] The sin halfangle formula

is always(?) taught as √(1-cos x)/√2. This fails outright for negative x, and numerically for small positive x. And impertinently imposes cosine for sine. Exercise: Find a nice formula for sin(x/2). Only in terms of sin x, good for -π/2 < x < π/2 (at least), and stable near 0. I had a he<<uva time rederiving it. I got a triangle wave when I plotted what I remembered. I was going to send you guys "Hey look at this triangle wave." After a slow, geriatric rederivation, I got the same bleeping triangle wave! The segments are imperceptibly curved! --rwg Plot this spoiler for -2π<x<2π: StringReverse@"\)]\)]\)]x[niS + 1\([xoBtrqS\* + ]\)]x[niS - 1\([xoBtrqS\*\( ,\)]x[niS\([xoBnoitcarF\*\(\!" Then plot the difference from sin(x/2).