# How to plot two functions together? [closed]

I have defined two function like f[Rp_] := Sin[0.5 ArcSin[Sqrt[(3 Rp^2)/((2 - Rp)^2 + 3 Rp^2)]]] and f[Rm_] := Sin[0.5 ArcSin[Sqrt[(3 Rm^2)/((2 + Rm)^2 + 3 Rm^2)]]].

Plotting them as Plot[(2/Sqrt[6]) f[Rp] (2/Sqrt[6]) f[Rp], {Rp, 0.0, 1.3}, PlotRange -> {{0, 1.3}, {0, .23}}, Frame -> True, FrameLabel -> {d/a, Subscript[Sin\[Theta], 13]}, PlotStyle -> Directive[Red, Thick], LabelStyle -> Directive[Black, Bold]]

and Plot[(2/Sqrt[6]) f[Rm], {Rm, 0.0, 1.3}, PlotRange -> {{0, 1.3}, {0, .23}}, Frame -> True, FrameLabel -> {d/a, Subscript[Sin\[Theta], 13]}, PlotStyle -> Directive[Red, Thick], LabelStyle -> Directive[Black, Bold]]

The outputs are as follows..... Mismatch between Axes -> True and Frame ->True

Now, How can I combine them, I've tried with Plot[{(2/Sqrt[6]) f[Rp], (2/Sqrt[6]) f[Rm]}, {Rm, Rp, 0.0, 1.3}, PlotRange -> {{0, 1.3}, {0, .23}}, Frame -> True, FrameLabel -> {d/a, Subscript[Sin\[Theta], 13]}, PlotStyle -> Directive[Red, Thick], LabelStyle -> Directive[Black, Bold]]

But I'm not getting properly. Probably I'm making mistake in {Rm, Rp, 0.0, 1.3}.

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## closed as too localized by Yves Klett, Sjoerd C. de Vries, Artes, Ajasja, whuberMay 9 '13 at 19:37

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The brute force method would be to store the two functioning outputs in variables  plot1 = Plot[(2/Sqrt[6]) f[Rp] (2/Sqrt[6]) f[Rp], {Rp, 0.0, 1.3}, PlotRange -> {{0, 1.3}, {0, .23}}, Frame -> True, FrameLabel -> {d/a, Subscript[Sin[Theta], 13]}, PlotStyle -> Directive[Red, Thick], LabelStyle -> Directive[Black, Bold]]  plot2 would be made the same way and then use  Show[{plot1, plot2}]  I'm confused by why you are making two identical functions, however. –  bobthechemist May 9 '13 at 13:58
Plot[{Sin[x], Sin[2 x], Sin[3 x]}, {x, 0, 2 Pi}, PlotLegends -> "Expressions"] is the second example in the help ffile for Plot. Mimic it. –  bill s May 9 '13 at 13:58
What are you trying to do? You have defined the function f twice. –  bill s May 9 '13 at 14:01
@bobthechemist, Two functions are different. f[Rp_] contains (2 - Rp) term where as f[Rm_] contains (2 + Rm) term. I have used 'Show[{plot1, plot2}]' and its works. Now how to fill the spaces between the curves like the code 'Filling -> {1 -> {{2}, Green}' in this case. –  Biswajit May 9 '13 at 14:12
Thanks @bills, I got it now. I made mistake in defining the functions. –  Biswajit May 9 '13 at 15:07

Bill s is right, you have simply overwritten the definition of f. The code below will show the two plots in one image.

f1[Rp_] := Sin[0.5 ArcSin[Sqrt[(3 Rp^2)/((2 - Rp)^2 + 3 Rp^2)]]]
f2[Rp_] := Sin[0.5 ArcSin[Sqrt[(3 Rp^2)/((2 + Rp)^2 + 3 Rp^2)]]]

plot1 =
Plot[(2/Sqrt[6]) f1[Rp], {Rp, 0.0, 1.3},
PlotRange -> {{0, 1.3}, {0, .23}}, Frame -> True,
FrameLabel -> {d/a, Subscript[Sin[\[Theta]], 13]},
PlotStyle -> Directive[Red, Thick],
LabelStyle -> Directive[Black, Bold]]

plot2 = Plot[(2/Sqrt[6]) f2[Rp], {R, 0.0, 1.3},
PlotRange -> {{0, 1.3}, {0, .23}}, Frame -> True,
FrameLabel -> {d/a, Subscript[Sin\[Theta], 13]},
PlotStyle -> Directive[Red, Thick],
LabelStyle -> Directive[Black, Bold]]

Show[plot1, plot2]


For filling the spaces between the curves

Plot[{(2/Sqrt[6]) f2[Rp], (2/Sqrt[6]) f1[Rp]}, {Rp, 0.0, 2.0},
PlotRange -> {{0, 2.0}, {0, .4}}, Frame -> True,
FrameLabel -> {d/a, Subscript[Sin\[Theta], 13]},
PlotStyle -> Directive[Blue], Filling -> {1 -> {{2}, Pink}},
LabelStyle -> Directive[Black, Bold]]

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Plot[{(2/Sqrt[6]) f1[x] (2/Sqrt[6]) f1[x], (2/Sqrt[6]) f2[x]}, {x, 0.0, 1.3}, PlotRange -> {{0, 1.3}, {0, .23}}, Frame -> True, FrameLabel -> {d/a, Subscript[Sin[[Theta]], 13]}, PlotStyle -> Directive[Red, Thick], LabelStyle -> Directive[Black, Bold], Filling -> {1 -> {{2}, Green}}] should give the filling you are looking for –  bobthechemist May 9 '13 at 14:31
Thank a lot @bobthechemist –  Biswajit May 9 '13 at 15:14
Thanks a lot @Jacob Akkerboom. Thank you all. Got my answer. –  Biswajit May 9 '13 at 15:16
@BiswajitKarmakar no problem. Sorry you got downvoted. –  Jacob Akkerboom May 9 '13 at 15:30
@bobthechemist Thanks for editing. I would approve, but as it is it your code will produce a beep because it does not like Sin[Theta]. Also I think the formatting of the code doesn't work. –  Jacob Akkerboom May 9 '13 at 15:32