PlotLegend assigns different sizes for plots

Question

I have two curves that I wanted to plot where each curve is composed of two functions. As an example, the first curve is the piecewise function $\rm{sin(x)}$ for $x \in [0,5]$ and $(x-5)+\rm{sin}(5)$ for $x \in [5,10]$.

My issue is when plotting it, the PlotLegend assigns a shorter line on the first curve (solid line) as opposed to the second curve (dashed line). How to fix this?

In addition, is there a way to place the legend inside the plot, in the lower right corner? It's better if there is a way to input coordinates for the position, say $(8,-2)$, so that it's easily adjustable.

p1 = Plot[Sin[x], {x, 0, 5}, Frame -> True, FrameLabel -> {"x", "y"}, LabelStyle -> Directive[Black, 20], PlotStyle -> {Black, Thickness[thickness]}, PlotPoints -> 500, PlotRange -> {{0, 10}, {-3, 3}}, PlotLegends -> Placed[{"Sin(x)"}, Right], AspectRatio -> 3/4, ImageSize -> Large];
p2 = Plot[(x - 5) + Sin[5], {x, 5, 10}, Frame -> True, FrameLabel -> {"x", "y"}, LabelStyle -> Directive[Black, 20], PlotStyle -> {Black, Thickness[thickness]}, PlotPoints -> 500, PlotRange -> {{0, 10}, {-3, 3}}, AspectRatio -> 3/4, ImageSize -> Large];
p3 = Plot[Cos[x], {x, 0, 5}, Frame -> True, FrameLabel -> {"x", "y"}, LabelStyle -> Directive[Black, 20], PlotStyle -> {Black, Dashed, Thickness[thickness]}, PlotPoints -> 500, PlotRange -> {{0, 10}, {-3, 3}}, PlotLegends -> Placed[{"Cos(x)"}, Right], AspectRatio -> 3/4, ImageSize -> Large];
p4 = Plot[(x - 5) + Cos[5], {x, 5, 10}, Frame -> True, FrameLabel -> {"x", "y"}, LabelStyle -> Directive[Black, 20], PlotStyle -> {Black, Dashed, Thickness[thickness]}, PlotPoints -> 500, PlotRange -> {{0, 10}, {-3, 3}}, AspectRatio -> 3/4, ImageSize -> Large];
Show[p1, p2, p3, p4]

Answer 1

The different lengths of lines in the legend is indeed weird – one might even consider this as a bug.

The problem is most easily solved if you use one Plot instead of combining many of them with Show (which seems to be the cause of troubles). Furthermore, you can use Piecewise to construct your functions.

For better clarity, I have removed options that are not part of the problem. Also, relative positioning of the legend can be done with Placed, if you want to provide absolute coordinates, use Inset.

f1 = Piecewise[{{Sin[x], 0 <= x <= 5}, {Sin[5] + (x - 5), 5 < x <= 10}}];
f2 = Piecewise[{{Cos[x], 0 <= x <= 5}, {Cos[5] + (x - 5), 5 < x <= 10}}];

Plot[{f1, f2}, {x, 0, 10}, PlotStyle -> {Black, {Black, Dashed}}, 
 PlotLegends -> Placed[{"sin(x)", "cos(x)"}, {.2, .8}]]

Answer 2

$Version

(* "13.2.1 for Mac OS X ARM (64-bit) (January 27, 2023)" *)

Clear["Global`*"]

Alternatively, for a fuller description of the curves in the legend, use ConditionalExpression

Plot[{
  ConditionalExpression[Sin[x], 0 <= x <= 5],
  ConditionalExpression[(x - 5) + Sin[5], 5 < x <= 10],
  ConditionalExpression[Cos[x], 0 <= x <= 5],
  ConditionalExpression[(x - 5) + Cos[5], 5 < x <= 10]},
 {x, 0, 10},
 PlotLegends -> Placed["Expressions", {.325, .7}]]

EDIT: For dashed lines

With[{cd = ColorData[97]},
 Plot[{
   ConditionalExpression[Sin[x], 0 <= x <= 5],
   ConditionalExpression[(x - 5) + Sin[5], 5 < x <= 10],
   ConditionalExpression[Cos[x], 0 <= x <= 5],
   ConditionalExpression[(x - 5) + Cos[5], 5 < x <= 10]},
  {x, 0, 10},
  PlotStyle -> {cd[1], cd[2], {cd[3], Dashed}, {cd[4], Dashed}},
  PlotLegends -> Placed["Expressions", {.325, .7}]]]