\documentclass{standalone}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{fourier}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\usetikzlibrary{intersections}

\begin{document}

\begin{tikzpicture}
\begin{axis}[
  axis lines=center, 
  axis equal,
  xlabel=$x$, 
  ylabel=$y$,
  domain=-2*pi:2*pi,
  ymin=-5,
  ymax=5, 
  xmin=-6.8, 
  xmax=6.8, 
  label style={font=\scriptsize},
  tick label style={font=\scriptsize},
  xtick={-2*pi, -(3/2)*pi,-pi, -(1/2)*pi, 1/2*pi, pi, 3/2*pi, 2*pi},
  xticklabels={$-2\pi$, $-\frac{3}{2}\pi$, $-\pi$, $-\frac{\pi}{2}$,
    $\frac{\pi}{2}$, $\pi$, $\frac{3}{2}\pi$, $2\pi$},
  minor xtick={-5*pi/4,-3*pi/4, -pi/4, pi/4, 3*pi/4, 5*pi/4},
  ytick={-4,-3,-2,-1,1,2,3,4},
  legend entries={$f(x)=\sin(x)$, $g(x)=x\cos(x)+1$},
  legend pos=south east,
  legend cell align=left,
  legend style={font=\scriptsize},
  fun/.style={thick, samples=80, smooth}
]
\addplot[name path=f1, fun] {sin(deg(x))};
\addplot[name path=f2, fun, gray!70] {x*cos(deg(x))+1};
\fill[name intersections={of=f1 and f2, name=p, total=\j}]
  \foreach \i in {1,...,\j} {(p-\i) circle (2pt)}; 
\end{axis}
\end{tikzpicture}

\end{document}