Graphs of Trigonometric Functions Using TiKz and PgfPlot
\begin
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\documentclass[border=15,multi={tikzpicture},convert=imagemagick]{standalone}
\usepackage[utf8]{inputenc}
\usepackage[svgnames,names]{xcolor}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usepackage[T2A,T1]{fontenc}
\usepackage{fourier}
\begin{document}
\begin{tikzpicture}[help lines/.style={black!50,very thin}]
\foreach \x in {-360,-270,-180,-90,+90,+180,+270,+360} \draw ({\x/90},-0.15) -- ({\x/90},+0.15) node[below=7] {$\x^\circ$};
\foreach \y in {-4,-3,-2,-1,+1,+2,+3,+4} \draw (-0.15,\y) -- (+0.15,\y) node[left=7] {$\y$};
\draw[help lines] (-4.25,-4.25) grid (4.25,4.25);
\draw[<->,thick] (-4.25,0)--(4.25,0) node[right] {$x$};
\draw[<->,thick] (0,-4.25)--(0,4.25) node[above] {$y$};
\draw[very thick,color=blue ] plot [domain={-360/90}:{360/90},smooth] (\x,{sin(90*\x)});
\draw[very thick,color=green] plot [domain={-360/90}:{360/90},smooth] (\x,{cos(90*\x)});
\foreach \i in {0,...,4} \draw[very thick,color=brown] plot [domain={(180*(\i-2)-atan(4)*ceil(\i/4))/90}:{(180*(\i-2)+atan(4)*ceil((4-\i)/4))/90},smooth] (\x,{tan(90*\x)});
\node[blue ] at (5,3) {$y = \sin x$};
\node[green] at (5,2) {$y = \cos x$};
\node[brown] at (5,1) {$y = \tan x$};
\end{tikzpicture}
\begin{tikzpicture}[help lines/.style={black!50,very thin}]
\foreach \x in {-360,-270,-180,-90,+90,+180,+270,+360} \draw ({\x/90},-0.15) -- ({\x/90},+0.15) node[below=7] {$\x^\circ$};
\foreach \y in {-4,-3,-2,-1,+1,+2,+3,+4} \draw (-0.15,\y) -- (+0.15,\y) node[left=7] {$\y$};
\draw[help lines] (-4.25,-4.25) grid (4.25,4.25);
\draw[<->,thick] (-4.25,0)--(4.25,0) node[right] {$x$};
\draw[<->,thick] (0,-4.25)--(0,4.25) node[above] {$y$};
\foreach \i in {0,...,3} \draw[very thick,color=blue ] plot [domain={(180*(\i-2)+asin(1/4))/90}:{(180*(\i-1)-asin(1/4))/90},smooth] (\x,{cosec(90*\x)});
\foreach \i in {0,...,4} \draw[very thick,color=green] plot [domain={(180*(\i-2)-acos(1/4)*ceil(\i/4))/90}:{(180*(\i-2)+acos(1/4)*ceil((4-\i)/4))/90},smooth] (\x,{sec(90*\x)});
\foreach \i in {0,...,3} \draw[very thick,color=brown] plot [domain={(180*(\i-2)+atan(1/4))/90}:{(180*(\i-1)-atan(1/4))/90},smooth] (\x,{cot(90*\x)});
\node[blue ] at (5,3) {$y = \csc x$};
\node[green] at (5,2) {$y = \sec x$};
\node[brown] at (5,1) {$y = \cot x$};
\end{tikzpicture}
\begin{tikzpicture}[help lines/.style={black!50,very thin}]
\foreach \x / \r in {-4/-2\pi,-3/-1\frac{1}{2}\pi,-2/-\pi,-1/-\frac{1}{2}\pi,+1/+\frac{1}{2}\pi,+2/+\pi,+3/+1\frac{1}{2}\pi,+4/+2\pi} \draw (\x,-0.15) -- (\x,+0.15) node[below=7] {$\r$};
\foreach \y in {-4,-3,-2,-1,+1,+2,+3,+4} \draw (-0.15,\y) -- (+0.15,\y) node[left=7] {$\y$};
\draw[help lines] (-4.25,-4.25) grid (4.25,4.25);
\draw[<->,thick] (-4.25,0)--(4.25,0) node[right] {$x$};
\draw[<->,thick] (0,-4.25)--(0,4.25) node[above] {$y$};
\draw[very thick,color=blue ] plot [domain={(-2*pi)*(2/pi))}:{(+2*pi)*(2/pi)},smooth] (\x,{sin(\x*pi/2 r)});
\draw[very thick,color=green] plot [domain={(-2*pi)*(2/pi))}:{(+2*pi)*(2/pi)},smooth] (\x,{cos(\x*pi/2 r)});
\foreach \i in {0,...,4} \draw[very thick,color=brown] plot [domain={((\i-2)*pi-rad(atan(4))*ceil(\i/4))*(2/pi)}:{((\i-2)*pi+rad(atan(4))*ceil((4-\i)/4))*(2/pi)},smooth] (\x,{tan(\x*pi/2 r)});
\node[blue ] at (5,3) {$y = \sin x$};
\node[green] at (5,2) {$y = \cos x$};
\node[brown] at (5,1) {$y = \tan x$};
\end{tikzpicture}
\begin{tikzpicture}[help lines/.style={black!50,very thin}]
\foreach \x / \r in {-4/-2\pi,-3/-1\frac{1}{2}\pi,-2/-\pi,-1/-\frac{1}{2}\pi,+1/+\frac{1}{2}\pi,+2/+\pi,+3/+1\frac{1}{2}\pi,+4/+2\pi} \draw (\x,-0.15) -- (\x,+0.15) node[below=7] {$\r$};
\foreach \y in {-4,-3,-2,-1,+1,+2,+3,+4} \draw (-0.15,\y) -- (+0.15,\y) node[left=7] {$\y$};
\draw[help lines] (-4.25,-4.25) grid (4.25,4.25);
\draw[<->,thick] (-4.25,0)--(4.25,0) node[right] {$x$};
\draw[<->,thick] (0,-4.25)--(0,4.25) node[above] {$y$};
\foreach \i in {0,...,3} \draw[very thick,color=blue ] plot [domain={((\i-2)*pi+rad(asin(1/4)))*(2/pi)}:{((\i-1)*pi-rad(asin(1/4)))*(2/pi)},smooth] (\x,{cosec(\x*pi/2 r)});
\foreach \i in {0,...,4} \draw[very thick,color=green] plot [domain={((\i-2)*pi-rad(acos(1/4))*ceil(\i/4))*(2/pi)}:{((\i-2)*pi+rad(acos(1/4))*ceil((4-\i)/4))*(2/pi)},smooth] (\x,{sec(\x*pi/2 r)});
\foreach \i in {0,...,3} \draw[very thick,color=brown] plot [domain={((\i-2)*pi+rad(atan(1/4)))*(2/pi)}:{((\i-1)*pi-rad(atan(1/4)))*(2/pi)},smooth] (\x,{cot(\x*pi/2 r)});
\node[blue ] at (5,3) {$y = \csc x$};
\node[green] at (5,2) {$y = \sec x$};
\node[brown] at (5,1) {$y = \cot x$};
\end{tikzpicture}
\begin{tikzpicture}
\begin{axis}[
axis lines=middle,
axis line style={thick,<->},
xmin=-2*pi-0.5,xmax=2*pi+0.5,ymin=-4.5,ymax=4.5,
ytick={-4,-3,-2,-1,1,2,3,4},
xtick={-2*pi,-1.5*pi,-pi,-0.5*pi,0,0.5*pi,pi,1.5*pi,2*pi},
xticklabels={$-2\pi$,$-\frac{3}{2}\pi$,$-\pi$,$-\frac{1}{2}\pi$,$0$,$+\frac{1}{2}\pi$,$+\pi$,$+\frac{3}{2}\pi$,$+2\pi$},
tick label style={font=\tiny},
grid=major,
major grid style={dashed,very thin,black},
every axis plot post/.append style={thick},
label style={font=\tiny},
xlabel=$x$,
ylabel=$y$,
smooth,
%clip=false,restrict y to domain=-4:4,
legend style={
font=\tiny,
legend cell align=left,
legend pos=outer north east,
draw=none,
empty legend},
legend entries={[blue]$y=\sin x$,[green]$y=\cos x$,[brown]$y=\tan x$}
]
\addplot[domain=-2*pi:2*pi,samples=200,blue]{sin(deg(x))};
\addplot[domain=-2*pi:2*pi,samples=200,green]{cos(deg(x))};
%\addplot[domain=-2*pi:2*pi,samples=200,brown]{tan(deg(x))};
\addplot[domain=-2 *pi:-1.5*pi,samples=200,brown]{tan(deg(x))};
\addplot[domain=-1.5*pi:-0.5*pi,samples=200,brown]{tan(deg(x))};
\addplot[domain=-0.5*pi: 0.5*pi,samples=200,brown]{tan(deg(x))};
\addplot[domain= 0.5*pi: 1.5*pi,samples=200,brown]{tan(deg(x))};
\addplot[domain= 1.5*pi: 2 *pi,samples=200,brown]{tan(deg(x))};
\end{axis}
\end{tikzpicture}
\begin{tikzpicture}
\begin{axis}[
axis lines=middle,
axis line style={thick,<->},
xmin=-2*pi-0.5,xmax=2*pi+0.5,ymin=-4.5,ymax=4.5,
ytick={-4,-3,-2,-1,1,2,3,4},
xtick={-2*pi,-1.5*pi,-pi,-0.5*pi,0,0.5*pi,pi,1.5*pi,2*pi},
xticklabels={$-2\pi$,$-\frac{3}{2}\pi$,$-\pi$,$-\frac{1}{2}\pi$,$0$,$+\frac{1}{2}\pi$,$+\pi$,$+\frac{3}{2}\pi$,$+2\pi$},
tick label style={font=\tiny},
label style={font=\tiny},
grid=major,
major grid style={dashed,very thin,black},
every axis plot post/.append style={semithick},
xlabel=$x$,
ylabel=$y$,
smooth,
%clip=false,restrict y to domain=-4:4,
legend style={
font=\tiny,
legend cell align=left,
legend pos=outer north east,
draw=none,
empty legend},
legend entries={[blue]$y=\sin x$,[green]$y=\cos x$,[brown]$y=\tan x$}
]
%\addplot[domain=-2*pi: 2*pi,samples=200,blue]{cosec(deg(x))};
\addplot[domain=-2 *pi: -pi,samples=200,blue]{cosec(deg(x))};
\addplot[domain= -pi: 0,samples=200,blue]{cosec(deg(x))};
\addplot[domain= 0: pi,samples=200,blue]{cosec(deg(x))};
\addplot[domain= pi: 2*pi,samples=200,blue]{cosec(deg(x))};
%\addplot[domain=-2 *pi: 2*pi,samples=200,green]{sec(deg(x))};
\addplot[domain=-2 *pi:-1.5*pi,samples=200,green]{sec(deg(x))};
\addplot[domain=-1.5*pi:-0.5*pi,samples=200,green]{sec(deg(x))};
\addplot[domain=-0.5*pi: 0.5*pi,samples=200,green]{sec(deg(x))};
\addplot[domain= 0.5*pi: 1.5*pi,samples=200,green]{sec(deg(x))};
\addplot[domain= 1.5*pi: 2 *pi,samples=200,green]{sec(deg(x))};
%\addplot[domain=-2*pi:2*pi,samples=200,brown]{cot(deg(x))};
\addplot[domain=-2 *pi: -pi,samples=200,brown]{cot(deg(x))};
\addplot[domain= -pi: 0,samples=200,brown]{cot(deg(x))};
\addplot[domain= 0: pi,samples=200,brown]{cot(deg(x))};
\addplot[domain= pi: 2*pi,samples=200,brown]{cot(deg(x))};
\end{axis}
\end{tikzpicture}
\end{document}
%-----------------------------------------------------------------------
% Muhammad Sahlan Rosyidi ibn Muhammad Chaizuddin Nuh Syuhada’
% http://creativecommons.org/licenses/by/4.0/
% ............., .. ................. .... . / .. ......... .... .
% Senin Pahing, 22 Rabī‘ Al-Ākhir 1422 H / 7 Desember 2020 M42
% ±22:10:00 PM (GMT + 07:00).
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