Graphics, Figures & Tables ⇒ Strangely looking trigonometric function plots?

[ziezi]

I'm trying to plot simple trigonometric functions,sin(x), sin^{2}(x), with the following code:

Code: Select all

\documentclass[a4paper]{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.14}

\begin{document}
\begin{tabular}{@{}c@{}}
\begin{tikzpicture}
	\begin{axis}[
		width = \axisdefaultwidth,
		height = 0.3\textheight,
		xlabel = $x$,
		ylabel = $\psi(x)$,
		title = {Wavefunction in periodic potential.},
		xmin = 0, xmax = 10,
		ymin = -1.2, ymax = 1.2,
		xtick = {0, 2, ..., 10},
        	xticklabels = {$0$, $a$, $2a$, $3a$, $4a$, $5a$},
	]

	\addplot [color = red, domain = 0 : 10, smooth]  plot {cos(deg(\x*pi))} 
		node [pos = 0.3, above right] {$cos(x)$};
	\addplot [color = blue, domain = 0 : 10, smooth]  plot {sin(deg(\x*pi))} 
		node [pos = 0.9, above left] {$sin(x)$};
	
	\addlegendentry{$\psi_{+}(x)$};
	\addlegendentry{$\psi_{-}(x)$};
	\end{axis}
\end{tikzpicture}
\\
\begin{tikzpicture}
	\begin{axis}[
		width = \axisdefaultwidth,
		height = 0.3\textheight,
		xlabel = $x$,
		ylabel = $\rho(x)$,
		title = {Probability density in periodic potential.},
		xmin = 0, xmax = 10,
		ymin = 0, ymax = 2.5,
		xtick = {0, 2, ...,10},
        	xticklabels = {$0$, $a$, $2a$, $3a$, $4a$, $5a$},
	]

	\addplot [color = red, domain = 0 : 10, smooth] plot {2*cos(deg(\x*pi))^2} 
		node [pos= 0.3, above right] {$cos^{2}(x)$};
	\addplot [color = blue, domain = 0 : 10, smooth] plot {2*sin(deg(\x*pi))^2} 
		node [pos = 0.9, above left] {$sin^{2}(x)$};
	
	\addlegendentry{$\rho_{+}(x)$};
	\addlegendentry{$\rho_{-}(x)$};
	\end{axis}
\end{tikzpicture}
\end{tabular}
\end{document}

and I get strange results. The plots are way off of what they should be, i.e. the $sin(x)$ and $cos(x)$ are not smooth and drifting on the y-axis. The $sin^{2}(x)$ and $cos^{2}(x)$ are horrendous.

The intended result is to plot 5 peaks where the cos(x) has its maximums over a, 2a, 3a, etc. similar to the grey plots.

Why are the plots like this? What am I doing wrong?

[Stefan Kottwitz]

Perhaps remove the factor pi in the argument:

Code: Select all

\addplot [color = red, domain = 0 : 10,  smooth]  plot {cos(deg(x))}
    node [pos = 0.3, above right] {$cos(x)$};
\addplot [color = blue, domain = 0 : 10, smooth]  plot {sin(deg(x))}
    node [pos = 0.9, above left] {$sin(x)$};

...

\addplot [color = red, domain = 0 : 10,  smooth] plot {2*cos(deg(x))^2}
    node [pos= 0.3, above right] {$cos^{2}(x)$};
\addplot [color = blue, domain = 0 : 10, smooth] plot {2*sin(deg(x))^2}
    node [pos = 0.9, above left] {$sin^{2}(x)$};

Stefan

[Stefan Kottwitz]

By the way, math operators are commonly written upright, not italic, there are macros for it:

Code: Select all

node [pos = 0.3, above right] {$\cos(x)$};
node [pos = 0.9, above left] {$\sin(x)$};

Stefan

[ziezi]

Thank you for the fast response!

You are right, removing pi from the argument makes things better, however, I don't know how to plot specific number of maximums, matched to specific points on the x-axis, corresponding with the maximums of the other plot below.

I've updated the question and included additional information.

[Stefan Kottwitz]

Try this, notice the xticks settings:

Code: Select all

\documentclass[a4paper]{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.14}
\pgfmathsetmacro{\PI}{pi}
\begin{document}
\begin{tikzpicture}
	\begin{axis}[
		width = \axisdefaultwidth,
		height = 0.3\textheight,
		xlabel = $x$,
		ylabel = $\rho(x)$,
		title = {Probability density in periodic potential.},
		xmin = 0, xmax = 16,
		ymin = 0, ymax = 2.5,
		scaled x ticks={real:\PI},
		xtick scale label code/.code={},
		xtick distance=pi,
	    	xticklabels = {,,$a$, $2a$, $3a$, $4a$, $5a$}
	]
 	\addplot [color = red, domain = 0 : 16, samples = 150, smooth] plot {2*cos(deg(x))^2} 
		node [pos= 0.3, above right] {$\cos^{2}(x)$};
	\addlegendentry{$\rho_{+}(x)$};
	\addlegendentry{$\rho_{-}(x)$};
	\end{axis}
\end{tikzpicture}
\end{document}

cos-plot.png (23.12 KiB) Viewed 4130 times

Stefan

[ziezi]

Thanks again for the suggestion! It worked great!

I hope that by clicking accept on the last answer I've closed/completed the question.

[Stefan Kottwitz]

Yes, that's perfect. Clicking the checkmark at that post that was the solution, marks the whole topic as solved (so supporters see it) and makes that solution the hyperlink when one clicks the checkmark at the top, so google searchers can jump to the solution.

Stefan