# Mathematica does not plot my expression

Mathematica does not plot the expression.

1/2 Sqrt[-(77/12) (72/77 + Cos[x/2]) - 2 Sqrt[5929/576 (72/77 + Cos[x/2])^2 -
77/4 (17/28 + Cos[x/2] + (43 Cos[x])/308)]]


Why not?

• Because there are imaginary parts in your expression. Try Plot[ Abs[1/2 Sqrt[-(77/12) (72/77 + Cos[x/2]) - 2 Sqrt[5929/576 (72/77 + Cos[x/2])^2 - 77/4 (17/28 + Cos[x/2] + (43 Cos[x])/308)]]],{x,0,4 Pi}] – andre314 Dec 17 '17 at 10:25
• But this is Absolute Value.I need real part but I could not use Re function in wolfram. – user54260 Dec 17 '17 at 11:11
• If I plot your function f = 1/2 Sqrt[-(77/12) (72/77 + Cos[x/2]) -2 Sqrt[5929/576 (72/77 + Cos[x/2])^2 -77/4 (17/28 + Cos[x/2] + (43 Cos[x])/308)]] in the complex plane ParametricPlot[{Re[f], Im[f]}, {x, -10, 10}] I get a strictly imaginary output, so the realpart Re[f]==0 seems to vanish !? – Ulrich Neumann Dec 17 '17 at 11:58
• Really,I dont know.But assume that Real part is zero.Why does mathematica not plot? – user54260 Dec 17 '17 at 13:11
• @user54260 : MMA plots a zero line, in the example I gave to you in my last comment , you see a straight line along the imaginary axes... – Ulrich Neumann Dec 17 '17 at 13:23

In such cases: take a look at your root. It has the form Sqrt[a[x]]-2b[x]] where b is again a root, then looking at the terms under the root(s):

a[x_] := -(77/12) (72/77 + Cos[x/2]);


and

    b[x_] := 5929/576 (72/77 + Cos[x/2])^2 -
77/4 (17/28 + Cos[x/2] + (43 Cos[x])/308);


then one can investigate separately:

Plot[{a[x], b[x]}, {x, -10, 10}]


delivers:

So we have only a small region (between 5 and 8) where b[x]is positive, but the overall value under the root is not:

Plot[a[x] - 2 Sqrt[b[x]], {x, 5, 8}, AxesOrigin -> {0, 0}]


so: No plot in the real plane.

reg = ParametricRegion[{Re[f[x]], Im[f[x]]}, {{x, -10, 10}}]

and then Region @ regdelivers: