How do I rotate labels in a plot?

Question

Consider the following plot:

Show[LogLogPlot[{x, x^2, x^1.5, 5/x}, {x, 0.5, 3}, 
  PlotRange -> {{0.5, 3}, {0.5, 10}}, Frame -> True, 
  FrameStyle -> Directive[Black, 25],
  PlotStyle -> {{Thick, Blue}, {Thick, Red}, {Thick, 
     Darker@Darker@Green}, {Thick, Blue}, {Thick, Blue, 
     Dashing[0.02]}, {Thick, Darker@Darker@Green, Dashing[0.02]}}, 
  ImageSize -> Large, FrameLabel -> {"x", "f(x)"}, 
  PlotLegends -> 
   Placed[{Style["Curve 1", 21], Style["Curve 2", 21], 
     Style["Curve 3", 21]}, {0.83, 0.15}], 
  Filling -> {1 -> {{4}, Directive[Blue, Opacity[0.1]]}, 
    4 -> {Top, Directive[Gray, Opacity[0.1]]}, 
    5 -> {Top, Directive[Gray, Opacity[0.1]]}}], 
 Graphics[{Text[Style["Domain 1", 20, Darker@Blue], 
    Scaled[{0.3, 0.5}]], 
   Text[Style["Domain 2", 22, Darker@Blue], Scaled[{0.7, 0.7}]]}]]

The result is

Could you please tell me how to rotate the legend "Domain 2" to make it collinear to the blue line?

P.S. Without the deformation of the text.

Answer 1

1. You can use the fourth argument of Text to control the direction of text:

LogLogPlot[{x, x^2, x^1.5, 5/x}, {x, 0.5, 3}, 
 PlotRange -> {{0.5, 3}, {0.5, 10}}, Frame -> True, 
 FrameStyle -> Directive[Black, 25], 
 PlotStyle -> {{Thick, Blue}, {Thick,Red}, {Thick, Darker@Darker@Green}, {Thick, Blue}},
 ImageSize -> Large, FrameLabel -> {"x", "f(x)"}, 
 PlotLegends -> Placed[{Style["Curve 1", 21], Style["Curve 2", 21], 
    Style["Curve 3", 21]}, {0.83, 0.15}], 
 Filling -> {1 -> {{4}, Directive[Blue, Opacity[0.1]]}, 
   4 -> {Top, Directive[Gray, Opacity[0.1]]}}, 
 Epilog -> {Text[Style["Domain 1", 20, Darker@Blue], Scaled[{0.3, 0.5}]], 
   Text[Style["Domain 2", 22, Darker@Blue], Scaled[{0.5, 0.75}], Center, {3, -1}]}]

2. You can have the text orientation determined by the curve it is associated with using a custom arrowhead:

LogLogPlot[{x, x^2, x^1.5, 5/x}, {x, 0.5, 3}, 
  PlotRange -> {{0.5, 3}, {0.5, 10}}, Frame -> True, 
  FrameStyle -> Directive[Black, 25], 
  BaseStyle -> Arrowheads[0], 
  PlotStyle -> {{Thick, Blue}, {Thick, Red}, {Thick, Darker @ Darker @ Green}, 
     {Thick, Blue, Arrowheads[{{Automatic, .5, 
       Graphics[Text[Style["Domain 2", 22, Darker@Blue], {0, 0}, {0, -1}]]}}]}}, 
  ImageSize -> Large, FrameLabel -> {"x", "f(x)"}, 
  PlotLegends -> Placed[{Style["Curve 1", 21], Style["Curve 2", 21], 
     Style["Curve 3", 21]}, {0.83, 0.15}], 
  Filling -> {1 -> {{4}, Directive[Blue, Opacity[0.1]]}, 
    4 -> {Top, Directive[Gray, Opacity[0.1]]}}, 
  Epilog -> {Text[Style["Domain 1", 20, Darker@Blue], Scaled[{0.3, 0.5}]]}] /. 
  Line -> Arrow

Answer 2

LogLogPlot[{x, x^2, x^1.5, 5/x}, {x, 0.5, 3},
 PlotRange -> {{0.5, 3}, {0.5, 10}},
 Frame -> True,
 FrameStyle -> Directive[Black, 25],
 PlotStyle -> {
   {Thick, Blue},
   {Thick, Red},
   {Thick, Darker@Darker@Green},
   {Thick, Blue},
   {Thick, Blue, Dashing[0.02]},
   {Thick, Darker@Darker@Green, Dashing[0.02]}},
 ImageSize -> Large,
 FrameLabel -> {"x", "f(x)"},
 PlotLegends -> Placed[{Style["Curve 1", 21], Style["Curve 2", 21],
    Style["Curve 3", 21]}, {0.83, 0.15}],
 Filling -> {1 -> {{4}, Directive[Blue, Opacity[0.1]]},
   4 -> {Top, Directive[Gray, Opacity[0.1]]},
   5 -> {Top, Directive[Gray, Opacity[0.1]]}},
 Epilog -> {Text[Style["Domain 1", 20, Darker@Blue], 
    Scaled[{0.3, 0.5}]],
   Inset[
    Graphics[
     Rotate[
      Text[Style["Domain 2", 22, Darker@Blue], Scaled[{0.45, 0.8}]],
      -20 Degree]],
    Scaled[{0.5, 0.6}]]}]

Answer 3

In case you are not aware, it is possible to interactively edit the plot output which is often the fastest way for a one-off solution.

If you hover over "Domain 2" in the output and double click you should see an editing frame:

Use the handles to rotate and position the label:

Then click outside the graphic and the edit is saved: