Try the option

Ticks -> {{#, # Pi} & /@ Range[8], Automatic}

A simple glance into the documentation would have done it ...

The tick specification {a, b} means that in position a we get the tick label b. In the case {Pi,Pi} the effect of is the same as simply Pi, you are right.

Quantity[3, "Degrees"] is replaced internally by Quantity[3, "AngularDegrees"], just the way Quantity[3, "s"] is replaced by Quantity[3, "Seconds"].

Now if I want to have on the y-axis something like that:

How can I do this?

ListPlot[{\!\(
\*SubscriptBox[\(\[Limit]\), \(n -> 
\*SuperscriptBox[\(1\), \(+\)]\)]\(ArcTan[
\*FractionBox[\(B[n]\), \(A[n]\)]]\)\), \!\(
\*SubscriptBox[\(\[Limit]\), \(n -> 
\*SuperscriptBox[\(2\), \(+\)]\)]\(ArcTan[
\*FractionBox[\(B[n]\), \(A[n]\)]]\)\), \!\(
\*SubscriptBox[\(\[Limit]\), \(n -> 
\*SuperscriptBox[\(3\), \(+\)]\)]\(ArcTan[
\*FractionBox[\(B[n]\), \(A[n]\)]]\)\), \!\(
\*SubscriptBox[\(\[Limit]\), \(n -> 
\*SuperscriptBox[\(4\), \(+\)]\)]\(ArcTan[
\*FractionBox[\(B[n]\), \(A[n]\)]]\)\), \!\(
\*SubscriptBox[\(\[Limit]\), \(n -> 
\*SuperscriptBox[\(5\), \(+\)]\)]\(ArcTan[
\*FractionBox[\(B[n]\), \(A[n]\)]]\)\), \!\(
\*SubscriptBox[\(\[Limit]\), \(n -> 
\*SuperscriptBox[\(6\), \(+\)]\)]\(ArcTan[
\*FractionBox[\(B[n]\), \(A[n]\)]]\)\), \!\(
\*SubscriptBox[\(\[Limit]\), \(n -> 
\*SuperscriptBox[\(7\), \(+\)]\)]\(ArcTan[
\*FractionBox[\(B[n]\), \(A[n]\)]]\)\), \!\(
\*SubscriptBox[\(\[Limit]\), \(n -> 
\*SuperscriptBox[\(8\), \(+\)]\)]\(ArcTan[
\*FractionBox[\(B[n]\), \(A[n]\)]]\)\)}, 
 PlotRange -> {{0*\[Pi], 2*\[Pi]}, Automatic}, Filling -> Axis, 
 Ticks -> {{#, # Pi} & /@ Range[8], Automatic}]

Mathematica 13.2 Notebook file attached.

Entire Code:

f5[x_] := \!\(\*
TagBox[GridBox[{
{"\[Piecewise]", GridBox[{
{"1", 
RowBox[{"0", "<", "x", "<", "1"}]},
{"0", 
RowBox[{"1", "<", "x", "<", "2"}]}
},
AllowedDimensions->{2, Automatic},
Editable->True,
GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{1.}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.84]}, 
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]}, 
Offset[0.2]}},
Selectable->True]}
},
GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{1.}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.35]}, 
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]}, 
Offset[0.2]}}],
"Piecewise",
DeleteWithContents->True,
Editable->False,
SelectWithContents->True,
Selectable->False,
StripWrapperBoxes->True]\)
Plot[f5[x], {x, 0, 2.5}, Exclusions -> None];
T = 2 - 0;
A0 = 2/T*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(-
\*FractionBox[\(T\), \(2\)]\), 
FractionBox[\(T\), \(2\)]]\(f5[x] \[DifferentialD]x\)\) // Simplify;
A[n_] = 2/T*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(-
\*FractionBox[\(T\), \(2\)]\), 
FractionBox[\(T\), \(2\)]]\(f5[x]*Cos[
\*FractionBox[\(2*\[Pi]*n*x\), \(T\)]] \[DifferentialD]x\)\) // 
   Simplify;
B[n_] = 2/T*\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(-
\*FractionBox[\(T\), \(2\)]\), 
FractionBox[\(T\), \(2\)]]\(f5[x]*Sin[
\*FractionBox[\(2*\[Pi]*n*x\), \(T\)]] \[DifferentialD]x\)\) // 
   Simplify;
s5[k_, x_] := A0/2 + \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(n = 1\), \(k\)]\((A[n]*Cos[
\*FractionBox[\(2*\[Pi]*n*x\), \(T\)]] + B[n]*Sin[
\*FractionBox[\(2*\[Pi]*n*x\), \(T\)]])\)\) // Simplify;

Plot[{f5[x], s5[11, x]}, {x, 0, 2}, Exclusions -> None, 
 PlotLegends -> "Expressions", 
 PlotStyle -> {Thickness[0.008], Thickness[0.005]}]

Show[ListPlot[Sqrt[A[n]^2 + B[n]^2] /. n -> {1, 2, 3, 4, 5, 6, 7, 8}, 
  PlotRange -> {{0*\[Pi], 2*\[Pi]}, Automatic}, Filling -> Axis, 
  Ticks -> {{#, # Pi} & /@ Range[8], Automatic}], 
 Plot[{Sqrt[A[1]^2 + B[1]^2], Sqrt[A[3]^2 + B[3]^2]}, {\[Omega], 0, 
   6*\[Pi]}]]

ListPlot[{\!\(
\*SubscriptBox[\(\[Limit]\), \(n -> 
\*SuperscriptBox[\(1\), \(+\)]\)]\(ArcTan[
\*FractionBox[\(B[n]\), \(A[n]\)]]\)\), \!\(
\*SubscriptBox[\(\[Limit]\), \(n -> 
\*SuperscriptBox[\(2\), \(+\)]\)]\(ArcTan[
\*FractionBox[\(B[n]\), \(A[n]\)]]\)\), \!\(
\*SubscriptBox[\(\[Limit]\), \(n -> 
\*SuperscriptBox[\(3\), \(+\)]\)]\(ArcTan[
\*FractionBox[\(B[n]\), \(A[n]\)]]\)\), \!\(
\*SubscriptBox[\(\[Limit]\), \(n -> 
\*SuperscriptBox[\(4\), \(+\)]\)]\(ArcTan[
\*FractionBox[\(B[n]\), \(A[n]\)]]\)\), \!\(
\*SubscriptBox[\(\[Limit]\), \(n -> 
\*SuperscriptBox[\(5\), \(+\)]\)]\(ArcTan[
\*FractionBox[\(B[n]\), \(A[n]\)]]\)\), \!\(
\*SubscriptBox[\(\[Limit]\), \(n -> 
\*SuperscriptBox[\(6\), \(+\)]\)]\(ArcTan[
\*FractionBox[\(B[n]\), \(A[n]\)]]\)\), \!\(
\*SubscriptBox[\(\[Limit]\), \(n -> 
\*SuperscriptBox[\(7\), \(+\)]\)]\(ArcTan[
\*FractionBox[\(B[n]\), \(A[n]\)]]\)\), \!\(
\*SubscriptBox[\(\[Limit]\), \(n -> 
\*SuperscriptBox[\(8\), \(+\)]\)]\(ArcTan[
\*FractionBox[\(B[n]\), \(A[n]\)]]\)\)}, 
 PlotRange -> {{0*\[Pi], 2*\[Pi]}, Automatic}, Filling -> Axis, 
 Ticks -> {{#, # Pi} & /@ Range[8], Automatic}]

Attachments:

Untitled-4.nb

There are two different graphs involved:

You combined both:

Thanks Gianluca Gorni.

I am not sure here for Ticks why we need to put in Table {kPi, kPi} instead of k*Pi, because the results are the same:

Is it necessary to put that {kPi, kPi}? Or is it enough only {k*Pi}?

And regarding the AngularDegree and Degree, what is the difference between these 2? (because the results between them seems to be equal...from what I can see):

Degree is of course Degree, and I think AngularDegree means radian (rad). And if we want Quantity to remain in Degree then we leave {k, -90, 0}, and if we want to put in Qunatity AngularDegree (which is Radian(Rad)) then we should put {k, -90Pi/180, 0Pi/180}, am I interpreting correctly? Do you know?

Try this input:

Quantity[3, "Degrees"] // FullForm

It is somewhat confusing.

I don't know what to say, Degree has an expression (Pi/180, which is ok), and AngularDegree has no expression, although it tells you in the result that Degree would be AngularDegree...

And then which one should I use further to represent the degree in calculations and in Ticks, Table, etc: AngularDegrees or Degrees? So as not to expect wrong results or misinterpretations by Mathematica...Which would be the most suitable or better option between the 2? Which option from the 2 would you choose if you had to choose?

But even when I put Degrees instead of AngularDegrees little o it still remained (I posted already this above):

It's strange because there are 2 different names that seem to represent the same thing. There should normally be some difference between them (if it exists)...but there might not be any difference as well. The question is only when we know that we have to use AngularDegrees instead of Degrees...

Gianluca Gorni Thank You anyway for your support in this hole topic (from the begginning)