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I want to add some kind of arrows (or some kind of function) on the x-axis (as depicted). if sin(x) is higher than bx, then arrow should point to the right, in the interval between its two intersection. A left arrow, if bx is higher than sin(x). Arrows should vary with change of paramters.

adding arrows

func[x_, b_] := b*x;
Manipulate[
 Plot[{a*Sin[x], func[x, b]}, {x, 0, 2 Pi}],
 {a, 1, 10}, {b, 0.5, 10}]
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  • $\begingroup$ Can you be more clear as to what you mean when Sin[x] greater than bx? For a=1 and b=0.5, at $x=1$ Sin[x]>bx at $x=4$ Sin[x]<bx. At the intersection Sin[x]==bx. At which point of x are you evaluating at? $\endgroup$ – I should change my Username Jul 7 '17 at 9:12
  • $\begingroup$ if i lower b or raise a, then the interval where sin[x] is greater than bx gets larger. Then the left arrow pointing to the right should get longer aswell (until sin[x] is lower than bx). There is no specific point of x where i am evaluating at. The arrow should vary with the parameters a and b. $\endgroup$ – Manuel Fülling Jul 7 '17 at 9:44
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Update 2: Dealing with question in the comments:

My original code is much longer and with multiple functions. I don't use the command Show in it. So if i add /. Line->Arrow all functions get an arrow. Is there a possibility to use /. Line ->Arrow separately on functions?

You can put the /. Line->Arrow piece after Plot[...], and specify Arrowheads[0] for the lines that you want to be rendered as Lines as part of the PlotStyle setting. For example:

Manipulate[Plot[{a*Sin[x], func[x, b], 
     ConditionalExpression[0, func[x, b] <= a Sin[x]], 
     ConditionalExpression[0, func[x, b] >= a Sin[x]]}, {x, 0, 2 Pi}, 
    PlotStyle -> {Directive[Thick, Arrowheads[0], ColorData[54, "ColorList"][[1]]], 
      Directive[Thick, Arrowheads[0], ColorData[54, "ColorList"][[2]]], 
      Directive[Red, Thick, Arrowheads[{0, .05}]], 
      Directive[Blue, Thick, Arrowheads[{-.05, 0}]]}] /. Line -> Arrow,
   {a, 1, 10}, {b, 0.5, 10}]

enter image description here

Note: In version 9, you don't have to use /. Line->Arrow trick. You can use functions to specify the PlotStyle and use ({Directive[Blue, Thick, Arrowheads[{-.05, 0}], Arrow@@#}&) in place ofDirective[Blue, Thick, Arrowheads[{-.05, 0}]`. But this method no longer works in newer versions.

Update: If you have Version 10 or newer versions, you can also use NumberLinePlot as Epilog:

Manipulate[Plot[{a*Sin[x], func[x, b]}, {x, 0, 2 Pi}, 
    Epilog -> First[NumberLinePlot[{a Sin[x] <= func[x, b], 
       a Sin[x] > func[x, b]}, {x, 0, 2 Pi},
      PlotStyle -> {Directive[Red, Thick, Arrowheads[{-.05, 0}]], 
         Directive[Blue, Thick, Arrowheads[{0, .05}]]}, 
      Spacings -> 0] /. Line -> Arrow]],
   {a, 1, 10}, {b, 0.5, 10}]

enter image description here

Original answer:

Manipulate[Show[Plot[{a*Sin[x], func[x, b]}, {x, 0, 2 Pi}], 
  Plot[{ConditionalExpression[0, func[x, b] <= a Sin[x]], 
        ConditionalExpression[0, func[x, b] >= a Sin[x]]}, {x, 0, 2 Pi}, 
    PlotStyle -> {Directive[Red, Thick, Arrowheads[{0, .05}]], 
      Directive[Blue, Thick, Arrowheads[{-.05, 0}]]}] /. Line -> Arrow], 
 {a, 1, 10}, {b, 0.5, 10}]

enter image description here

You can also use a combination of Epilog and ParametricPlot with Mesh options:

Manipulate[Plot[{a*Sin[x], func[x, b]}, {x, 0, 2 Pi}, 
  Epilog -> First[ParametricPlot[{x, 0}, {x, 0, 2 Pi}, 
      MeshFunctions -> {a Sin[#] - func[#, b] &}, Mesh -> {{0}}, 
      MeshShading -> {Directive[Red, Thick, Arrowheads[{-.05, 0}]], 
        Directive[Blue, Thick, Arrowheads[{0, .05}]]}] /. Line -> Arrow]], 
  {a, 1, 10}, {b, 0.5, 10}]
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  • $\begingroup$ Can you explain a bit of how the ConditionalExpression[] is working? It returns 0 when func[x,b]<=a Sin[x] and 0 when func[x,b]>=a Sin[x]. Since the 2nd argument to ConditionalExpression[] is the cond., I can't seem to be able to wrap my head around how you are getting the coordinates. $\endgroup$ – I should change my Username Jul 7 '17 at 10:49
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    $\begingroup$ @IshouldchangemyUsername, ConditionalExpression[0,condition] gives 0 if the condition is satisfied and Nothing otherwise. The Nothing portion is not plotted so we get, in the current case, a line from {0,0} to {0,x*} where x* is the maximum point where condition is satisfied. BTW, ConditionalExpression[0,condition] gives the same result as Piecewise[{{0,condition}}, Nothing] (which may be more intuitive). Hope this helps. $\endgroup$ – kglr Jul 7 '17 at 10:57
  • $\begingroup$ ConditionalExpression[0, func[x, b] <= a Sin[x] is a condition where i only compare two functions with each other. What if i need to compare func[x,b] with two functions (for example with asin(x) and acos(x)? ConditionalExpression[0, func[x, b] <= {a Sin[x], a Cos[x]} does not work $\endgroup$ – Manuel Fülling Jul 7 '17 at 11:37
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    $\begingroup$ @Manuel, condition in ConditionalExpression[0,condition] should be a Boolean function that evaluates to True or False. So, you can use And @@ Thread[func[x, b] <= {a Sin[x], a Cos[x]}] or Or @@ Thread[func[x, b] <= {a Sin[x], a Cos[x]}] as condition in ConditionalExpression[0,condition] $\endgroup$ – kglr Jul 7 '17 at 11:59
  • $\begingroup$ if i add /. Line -> Arrow after my closing Plot Bracket ] , all my function get an arrow. Where do i add /. Line -> Arrow and do i need the command Show[] for it? $\endgroup$ – Manuel Fülling Jul 7 '17 at 14:17
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Another solution using NSolve to find the intersection point and Graphics to draw the arrows:

func[x_, b_] := b*x;
Manipulate[
 With[{xIntersection = 
    NSolve[{a*Sin[x] == func[x, b], x > 0}, x, Reals][[1, 1, 2]]},
  Show[
   Plot[{a*Sin[x], func[x, b]},
    {x, 0, 2 Pi},
    PlotRange -> {{0, 2 Pi}, {-6, 6}}
    ],
   Graphics[{
     Point@{xIntersection, func[xIntersection, b]},
     Arrowheads@0.03,
     Red, Arrow@{{0, 0}, {xIntersection, 0}},
     Blue, Arrow@{{2 Pi, 0}, {xIntersection, 0}}
     }]
   ]
  ],
 {a, 1, 10}, {b, 0.5, 10}
 ]

enter image description here

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