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I am providing the code for graphing three trigonometric functions. (In the preamble, I had to put a % before the command \usetikzlibrary{calc,angles,quotes} because LaTeX could not compile it with the command. It gave me the error can't find file 'tikzlibraryangles.code.tex'. MikTeX2.9 is compiling the code.) How do I add the labels "$\scriptstyle{y = \sin(x)}," "$\scriptstyle{y = \cos(x)}," and "$\scriptstyle{y = \tan(x)}" directly under the y-axis to the corresponding graphs? Arrowheads should be at both ends of the axes. They are currently at one end. Is there a code for putting labels (in nodes) for the tick marks over other features of the graphs? How does the code instruct TikZ to marks the tick marks in half-unit increments? How do I get the code to instruct TikZ to mark the tick marks in increments of integral multiples of \pi/2? In the graphs of the tangent function, the asymptotes are solid lines. How do I get dotted lines? In the code for graphing the tangent function, there is "scaled x ticks={real:3.1415}, xtick scale label code/.code={}". What does "{real:3.1415}" and "code/.code={}" instruct TikZ to draw on the x-axis?

\documentclass{article} \usepackage{amsmath} \usepackage{tikz} %\usetikzlibrary{calc,angles,quotes} \usepackage{pgfplots} \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={ $-2\pi$, $-3\pi/2$, $-\pi$, $\pi/2$, $\pi/2$, $\pi$, $3\pi/2$, $2\pi$ } ] \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={ $-2\pi$, $-3\pi/2$, $-\pi\hspace{0.30cm}$, $\pi/2$, $\pi/2$, $\pi\hspace{0.10cm}$, $3\pi/2$, $\hspace{0.25cm} 2\pi$ } ] \addplot [mark=none, ultra thick, red] {cos(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={}, ] \addplot [mark=none, thin, brown] {tan(deg(x))}; \end{axis} \end{tikzpicture} \end{document}
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You've asked quite a few questions! It's generally best to ask one, focused question on this site ;)

But, here's an attempt to get through your questions....

Labels, such as $y = \sin(x), would make the graphs more presentable. I guess directly under the y-axis.

You could use, for example,

\begin{axis}[ Axis Style, xtick={ -6.28318, -4.7123889, -3.14159, -1.5708, 1.5708, 3.14159, 4.7123889, 6.28318 }, xticklabels={ $-2\pi$, $-3\pi/2$, $-\pi$, $\pi/2$, $\pi/2$, $\pi$, $3\pi/2$, $2\pi$ }, ylabel={$y=\sin(x)$}, %<---- new bit ]

or else, for example,

... \addplot [mark=none, ultra thick, blue] {sin(deg(x))}; \addlegendentry{$y=\sin(x)$} %<---- new bit ...

You might also want to adjust the legend position using legend pos=...

Arrowheads should be at both ends of the axes. They are currently at one end.

You can use,

\pgfkeys{/pgfplots/Axis Style/.style={ width=.3\textwidth, %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, axis line style=<->, %<----- new bit }}

or otherwise use pgfplotsset (as demonstrated below).

The scale is suitable for the graphs of the sine and cosine functions but not for the tangent function. Maybe have the y-axis include -10 and 10.

Try using, for example,

\begin{axis}[ Axis Style, xtick={-6.28318, -4.7123889, ..., 6.28318}, scaled x ticks={real:3.1415}, xtick scale label code/.code={}, ymin=-10,ymax=10, %<---- new bit ]

Changing the scale for this graph may have the labels along the axes drawn over by the graph of the tangent function. Is there a code for putting labels (in nodes) over other features of a graph?

I believe you want the axis on top key for this.

Currently, the y-axes of the three graphs are aligned. How can I have the x-axes are aligned?

Remove the blank lines between your figures - note that you'll need to adjust the text width to get them to fit nicely - consider the geometry package for this.

What does mark=none instruct TikZ to do? What other options are there for mark?

mark=none means that you only get the curve, and not circles (or other marks) at the sample points along the way. There are a lot of other options - see Section 4.7 of the pgfplots for details.

Here's a complete bit of code to play with that implements the things I have mentioned. 

% arara: pdflatex % !arara: indent: {overwrite: yes} \documentclass{article} \usepackage{pgfplots} \usepackage[margin=1cm]{geometry} \pgfplotsset{Axis Style/.style={ width=.3\textwidth, %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, axis line style=<->, }} \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={ $-2\pi$, $-3\pi/2$, $-\pi$, $\pi/2$, $\pi/2$, $\pi$, $3\pi/2$, $2\pi$ }, ylabel={$y=\sin(x)$}, ] \addplot [mark=none, ultra thick, blue] {sin(deg(x))}; \addlegendentry{$y=\sin(x)$} \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={ $-2\pi$, $-3\pi/2$, $-\pi\hspace{0.30cm}$, $\pi/2$, $\pi/2$, $\pi\hspace{0.10cm}$, $3\pi/2$, $\hspace{0.25cm} 2\pi$ } ] \addplot [mark=none, ultra thick, red] {cos(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={}, ymin=-10,ymax=10, ] \addplot [mark=none, ultra thick, brown] {tan(deg(x))}; \end{axis} \end{tikzpicture} \end{document}
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An easy-to-customize template with PSTricks. 

\documentclass[pstricks,border=0pt,12pt,dvipsnames]{standalone} \usepackage{amsmath} \usepackage{pstricks-add} \usepackage{pst-plot} % \usepackage{pst-math} provides ATAN \usepackage[nomessages]{fp} \FPeval\XMin{0-2*pi} \FPeval\XMax{2*pi} \FPeval\YMin{0-pi} \FPeval\YMax{5*pi/3} \FPeval\XOL{0-1/3} % of DeltaX \FPeval\XOR{1/3} % of DeltaX \FPeval\YOB{0-1/3} % of DeltaY \FPeval\YOT{1/3} % of DeltaY \FPset\TrigLabelBase{3} \FPeval\DeltaX{pi/TrigLabelBase} \FPeval\DeltaY{pi/TrigLabelBase} \FPeval\AxisL{XMin+DeltaX*XOL} \FPeval\AxisR{XMax+DeltaX*XOR} \FPeval\AxisB{YMin+DeltaY*YOB} \FPeval\AxisT{YMax+DeltaY*YOT} \newlength\Width\Width=12cm \newlength\Height\Height=8cm \newlength\llx\llx=-5pt \newlength\urx\urx=15pt \newlength\lly\lly=-5pt \newlength\ury\ury=15pt \psset { llx=\llx, lly=\lly, urx=\urx, ury=\ury, xtrigLabels=true, ytrigLabels=true, trigLabelBase=\TrigLabelBase, labelFontSize=\scriptstyle, xAxisLabel=$x$, yAxisLabel=$y$, algebraic, plotpoints=500, } \def\f{Pi*sin(x)} \def\fp{Derive(1,\f)} \def\g{2*asin(x/(2*Pi))} \begin{document} \pslegend[lt]{% \color{NavyBlue}\rule{12pt}{1pt} & \color{NavyBlue} $y=\pi\sin x$ \\ \color{Red}\rule{12pt}{1pt} & \color{Red} $y=\pi\cos x$ \\ \color{ForestGreen}\rule{12pt}{1pt} & \color{ForestGreen} $y=2\sin^{-1}\left(\tfrac{x}{2\pi}\right)$ } \begin{psgraph} [ dx=\DeltaX, dy=\DeltaY, linecolor=gray, tickcolor=gray, ticksize=-3pt 3pt, axespos=top, ]{<->}(0,0)(\AxisL,\AxisB)(\AxisR,\AxisT){\dimexpr\Width-\urx+\llx}{!}%{\dimexpr\Height-\ury+\lly} \psaxes [ dx=\DeltaX, dy=\DeltaY, labels=none, subticks=5, tickwidth=.4pt, subtickwidth=.2pt, tickcolor=Red!30, subtickcolor=ForestGreen!30, xticksize=\YMin\space \YMax, yticksize=\XMin\space \XMax, subticksize=1, ](0,0)(\XMin,\YMin)(\XMax,\YMax) \psplot[linecolor=NavyBlue]{\XMin}{\XMax}{\f} \psplot[linecolor=Red]{\XMin}{\XMax}{\fp} \psplot[linecolor=ForestGreen]{\XMin}{\XMax}{\g} % ------------------- % tangent and normal \psplotTangent[linecolor=Magenta]{Pi 3 div 2 mul}{1.5}{\f} \psplotTangent[linecolor=Cyan,Derive={-1/\fp}]{Pi 3 div 2 mul}{1.5}{\f} % % sum \psplot[linecolor=Rhodamine]{\XMin}{\XMax}{Sum(i,0,1,7,(-1)^(i)*x^(2*i)/fact(2*i))} \end{psgraph} \end{document}

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Documentation

This section explains the settings used in the template.

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