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plotting - Axes labels as multiples of $pi$


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




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


enter image description here


Have fun!


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