[Tex/LaTex] Axis with trigonometric labels in PGFPlots

pgfplots

How do I make the axis labels use multiples of \pi in PGFPlots?
enter image description here

Best Answer

As mentioned in the comments, this is basically the same as Pgfplots with custom axis markers. All you need to do is to specify where you want the xtick={...} and how you want each of them labelled via xticklabels={...}.

Method 1: Explicit Labels:

Explicit labels can be specified using xticklabels. The one complication that comes about is that sometimes the label overlaps with the plot as is the case for -\pi and 2pi in the blue graph. I have not found a elegant way to fix that so I just manually add some spacing to those labels to tweak them as I did the red graph:

enter image description here

Method 2: Scaled Axis Labels:

An alternate is to scale the x-axis labels in terms of multiples of pi, and show that the x axis labels are multiples of pi. This solution is based on Spikes solution, so you should up vote that if you prefer this version. I prefer to label this as part of the axis (brown graph), but others might prefer to display it as in the cyan graph:

enter image description here

xticklabels:

If you want a tick mark, but not a corresponding label you can simply place an empty label as in $$ or just better just use a double comma ,, to skip it being labelled. For instance, if the labels at +\pi and -\pi are not desired, simply replace those labels with spaces (extra spaces here are just to point out where the gap is):

xticklabels={$-2\pi$, $-\frac{3\pi}{2}$,    , $-\frac{\pi}{2}$, 
             $\frac{\pi}{2}$,     , $\frac{3\pi}{2}$, $2\pi$}

xtick:

Note that two methods of specifying where the tick marks go are used in the code. One is to explicitly list them as

xtick={-6.28318, -4.7123889, -3.14159, -1.5708, 1.5708, 3.14159, 4.7123889, 6.28318}

This is used in the first two examples so that the correspondence between the xtick and xticklabels is easier to see. The second two use the more compact method:

xtick={-6.28318, -4.7123889, ..., 6.28318}

Code:

\documentclass{article} 
\usepackage{pgfplots}

% Grouping the common style settings here to make the code below easier to read
\pgfkeys{/pgfplots/Axis Style/.style={
    width=13.5cm, height=5cm,
    axis x line=center, 
    axis y line=middle, 
    samples=100,
    ymin=-1.5, ymax=1.5,
    xmin=-7.0, xmax=7.0,
    domain=-2*pi:2*pi
}}

\begin{document}
\begin{tikzpicture}
\begin{axis}[
    Axis Style,
    xtick={
        -6.28318, -4.7123889, -3.14159, -1.5708,
        1.5708, 3.14159, 4.7123889, 6.28318
    },
    xticklabels={
        $-2\pi$, $-\frac{3\pi}{2}$, $-\pi$, $-\frac{\pi}{2}$,
        $\frac{\pi}{2}$, $\pi$, $\frac{3\pi}{2}$, $2\pi$
    }
]
\addplot [mark=none, ultra thick, blue] {sin(deg(x))};
\end{axis}
\end{tikzpicture}

\begin{tikzpicture}
\begin{axis}[
    Axis Style,
    xtick={
        -6.28318, -4.7123889, -3.14159, -1.5708,
        1.5708, 3.14159, 4.7123889, 6.28318
    },
    xticklabels={
        $-2\pi$, $-\frac{3\pi}{2}$, $-\pi\hspace{0.30cm}$, $-\frac{\pi}{2}$,
        $\frac{\pi}{2}$, $\pi\hspace{0.10cm}$, $\frac{3\pi}{2}$, $\hspace{0.25cm} 2\pi$
    }
]
\addplot [mark=none, ultra thick, red] {sin(deg(x))};
\end{axis}
\end{tikzpicture}

\begin{tikzpicture}
\begin{axis}[
    Axis Style,
    xtick={-6.28318, -4.7123889, ..., 6.28318},
    scaled x ticks={real:3.1415},
    xtick scale label code/.code={},
    xlabel={$x \thinspace [\times \pi]$}
]
\addplot [mark=none, ultra thick, brown] {sin(deg(x))};
\end{axis}
\end{tikzpicture}

\begin{tikzpicture}
\begin{axis}[
    Axis Style,
    xtick={-6.28318, -4.7123889, ..., 6.28318},
    scaled x ticks={real:3.1415},
    xtick scale label code/.code={$[\times \pi]$},
    xlabel={$x$}
]
\addplot [mark=none, ultra thick, cyan] {sin(deg(x))};
\end{axis}
\end{tikzpicture}
\end{document}
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