Axes labels as multiples of $\pi$

Question

I have a list as containing seven elements:

list={0, 
     Cos[t/4] + Cos[(3 t)/4] + I (Sin[t/4] -  Sin[(3t)/4]),
      0,
     -Cos[t/4] - Cos[(3 t)/4] + I (Sin[t/4] +  Sin[(3t)/4]),
      0,
      +Cos[5t/4] - Cos[(3 t)/4] + I (Sin[5t/4] +  Sin[(3t)/4]),
      Cos[5t/4] - Cos[(3 t)/4] + I (Sin[5t/4] -  Sin[(3t)/4])
      }

I want to plot Abs[list[[2]]*list[[4]]], Abs[list[[2]]*list[[6]]], Abs[list[[2]]*list[[7]]] from {t,0,8 pi} just in one plot.

I used

Plot[{Abs[list2[[2]]*list2[[3]]], Abs[list2[[2]]*list2[[5]]], 
  Abs[list2[[2]]*list2[[9]]]}, {t, 0, 8 π} 
]

but the problem is: my favorite situation is scaling the 'x' axes with multiple of pi, for example: pi/6, pi/4, pi/3, pi/2, 5pi/6, 3pi/4, 2pi/3, pi and ... 8 pi.

However, they are not in the similar interval (Pi/6-0 != pi/4-pi/6) and I want to show them with the symbol of pi (Esc pi Esc) on the x axes. Has anyone had an experience with this?

Answer 1

Try this:

    list = {0, Cos[t/4] + Cos[(3 t)/4] + I (Sin[t/4] - Sin[(3 t)/4]), 
  0, -Cos[t/4] - Cos[(3 t)/4] + I (Sin[t/4] + Sin[(3 t)/4]), 
  0, +Cos[5 t/4] - Cos[(3 t)/4] + I (Sin[5 t/4] + Sin[(3 t)/4]), 
  Cos[5 t/4] - Cos[(3 t)/4] + I (Sin[5 t/4] - Sin[(3 t)/4])};


Plot[Abs[list[[2]]*list[[4]]], {t, 0, 8 \[Pi]}, 
 Ticks -> {{\[Pi]/6, 3 \[Pi]/4, 2 \[Pi], 4 \[Pi], 6 \[Pi], 8 \[Pi]}, 
   Automatic}]

yielding

Have fun!

Answer 2

I found the solution I was looking for at https://stackoverflow.com/questions/8936579/labeling-a-plot-in-increments-of-pi.

example:

Plot[Sin[x], {x, -Pi, Pi}, Ticks -> {Range[-Pi, Pi, Pi/4], Automatic}]

Credits go to Nasser.

Answer 3

You could join lists of tick positions:

ticks = Union @@ Table[Range[0, 8 Pi, dt], {dt, {Pi/6, Pi/4}}];

For such a long interval, this does not produce legible ticks:

Plot[{
  Abs[list2[[2]]*list2[[3]]],
  Abs[list2[[2]]*list2[[5]]],
  Abs[list2[[2]]*list2[[7]]]},
 {t, 0, 8 π},
 Ticks -> {ticks, Automatic}, PlotRange -> All]

You could pick a set of larger values for dt in the Table above. You could also use Solve to mark interesting features, but in this case, the numbers make unwieldy tick labels:

ticks = t /. Solve[0 < t <= 8 Pi && list2[[2]]*list2[[7]] == 0, t];
(*
  {4 π, 8 π, -8 ArcTan[1 - Sqrt[2]], 
   8 π + 8 ArcTan[1 - Sqrt[2]], 8 π - 8 ArcTan[1 + Sqrt[2]], 
   8 ArcTan[1 + Sqrt[2]]}
*)