Trig books give (c104) HALFANGLES(SIN(X/2)); sqrt(1 - cos(x)) (d104) ---------------- sqrt(2) Mathematica doesn't even bother. Drawbacks: It's in terms of cos instead of sin, and numerically rancid for small x. I like Plot[Sin[x/2] - Sin[x]/(Sqrt[1 - Sin[x]] + Sqrt[1 + Sin[x]]), {x, -1.6, 1.6}], which misleadingly portrays floating point noise until Plot[Sin[x/2] - Sin@x/(√(1 - Sin@x) + √(1 + Sin@x)), {x, -1.6, 1.6},PlotRange -> All] reveals __________________________________________/ / You can actually paste the above Plot commands into https://lab.open.wolframcloud.com/objects/wpl/GetStarted.nb to see them. —rwg