## LaTeX forum ⇒ Graphics, Figures & Tables ⇒ Strangely looking trigonometric function plots? Topic is solved

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ziezi
Posts: 3
Joined: Mon Sep 17, 2018 5:02 pm

### Strangely looking trigonometric function plots?

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

\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?
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Last edited by ziezi on Mon Sep 17, 2018 5:39 pm, edited 1 time in total.

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Stefan Kottwitz
Posts: 9285
Joined: Mon Mar 10, 2008 9:44 pm
Perhaps remove the factor pi in the argument:

\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
Posts: 9285
Joined: Mon Mar 10, 2008 9:44 pm
By the way, math operators are commonly written upright, not italic, there are macros for it:

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

Stefan

ziezi
Posts: 3
Joined: Mon Sep 17, 2018 5:02 pm
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
Posts: 9285
Joined: Mon Mar 10, 2008 9:44 pm
Try this, notice the xticks settings:

\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 408 times

Stefan

ziezi
Posts: 3
Joined: Mon Sep 17, 2018 5:02 pm
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