missing a tick label that has been named

Question

So I made this graph, and this graph can't show me the tick $\frac{5}{2}\pi$ at 7.85.

I've tried to enlarge the x max range, give extra ticks (and extra tick label) but nothing works. Anyone can help me? Thanks!

\documentclass[10pt,openany,a4paper]{article}
\usepackage[margin=1.5cm]{geometry}
\usepackage{a4wide}
\usepackage{amsfonts,amsmath,amssymb}
\usepackage{array}
\usepackage{tikz}
\usepackage{pgf}
\usepackage{pgfplots}
\pgfplotsset{compat=1.13}
\usepackage{mathrsfs}
\usetikzlibrary{arrows}
\usetikzlibrary{calc,angles,positioning,intersections,quotes,decorations.markings}
\usepackage{tkz-euclide}
\usepackage[utf8]{inputenc}
\usepackage{xcolor}
\usepackage[english]{babel}

\begin{document}

\begin{tikzpicture}
    \begin{axis} [
        axis line style = thick,
        axis x line = middle,
        axis y line = middle,
        xtick = {-3.14, -1.57, 0., ..., 7.85, 9.42},
        ytick = {-1, 0, 1},
        xlabel = {$\theta$},
        ylabel = {$y$},
        xticklabels = {$-\pi$, $-\frac{\pi}{2}$, , $\frac{\pi}{2}$, $\pi$, $\frac{3\pi}{2}$, $2\pi$, $\frac{5\pi}{2}$, $3\pi$},
        xmin = -3.5, xmax = 10,
        ymin = -1.5, ymax = 1.5,
        font = \tiny,
    ]

    \addplot[black, thin, samples = 1000, smooth, domain=-3.14:0] {cos(deg(x))};
    \addplot[cyan, thin, samples = 1000, smooth, domain=0:3.140000] {cos(deg(x))};
    \addplot[black, thin, samples = 1000, smooth, domain=3.14:8.5] {cos(deg(x))};
    \end{axis}
\end{tikzpicture}
\end{document}

Answer 1

By lucky chance, you could get your desired list of ticks if you'd remove some of the intermediate values and use xtick = {-3.14, -1.57, ..., 9.42}.

Why does this work? The above list will be expanded to

-3.14 
-1.57 
-0.00002 
1.56998 
3.13997 
4.70996 
6.27995 
7.84995 
9.41994

As you can see, the floating point precision of pgf is not that good. By pure luck, the last tikz is calculated to be 9.41994, which is lower than the upper boundary set to 9.42.

The list from your question, xtick = {-3.14, -1.57, 0., ..., 7.851, 9.42}, evaluates to

-3.14 
-1.57
0.
1.57 
3.14001 
4.71002 
6.28003 
9.42

Notice the absence of a value around 7.85. This tick is missing because pgf would calculate the next step in the list to be 7.85004, which is above the upper limit of 7.85.

You could avoid the problem by leaving a bit of margin for rounding errors with xtick = {-3.14, -1.57, 0., ..., 7.851, 9.42}.