Draw tangent line on a curve

Question

I would like to draw a tangent line on (x0) which is an intersection between vertical line and the red curve, this is my code

\documentclass[tikz,preview,border=1mm]{standalone}
\usetikzlibrary{calc,intersections,arrows}
\def\w{0.7}
\begin{document}
\begin{tikzpicture}[>=latex]
\draw[->,line width=0.5pt](-0.3,0) -- (5.2,0);
\draw[->,line width=0.5pt](0,-0.3) -- (0,3.5);
\draw[name path=curve,red] plot[samples=100,smooth,domain=0:3,variable=\t] 
({1+cos(deg(\w* \t)) * 5},{5+- sin(deg(\w\t))  \w* 5});
\drawname path=vline--+(90:3);
\path[name intersections={of=curve and vline, by=x0}];

\fill (x0) circle(1pt);
\end{tikzpicture}
\end{document}

Maybe https://tex.stackexchange.com/questions/37866/how-to-draw-tangent-vectors-and-component-vectors-on-a-curve can help? — Rmano, Jan 30 '24 at 15:09
Thanks, but this is not the case, I tried to adopt it with my problem and still nor working! — Hariz Khaled, Jan 30 '24 at 15:19
This would be much easier with a linear equation where you at least can set x or y to one specific value. — Jasper Habicht, Jan 30 '24 at 17:18
I treid to adapt https://tex.stackexchange.com/a/477208/38080 but I have a "Dimension too large..." error — Rmano, Jan 30 '24 at 17:19

Rmano · Answer 1 · 2024-02-01T07:05:42.523

If you can get away with the "smooth" part (which creates numerical instabilities), this (from https://tex.stackexchange.com/a/477208/38080) works:

\documentclass[tikz,preview,border=1mm]{standalone}
\usepackage{pgfplots}\pgfplotsset{compat=newest}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{calc,intersections,arrows}
\usetikzlibrary{decorations.markings}
\tikzset{tangent at/.style={% cf. https://tex.stackexchange.com/questions/25928/how-to-draw-tangent-line-of-an-arbitrary-point-on-a-path-in-tikz/25940#25940
        decoration={ markings,
            mark =at position #1 with {\draw[purple,-latex](0,0) -- (-1,0);},
        }, decorate
    }
}
\def\w{0.7}
\begin{document}
\begin{tikzpicture}[>=latex]
\draw->,line width=0.5pt -- (5.2,0);
\draw->,line width=0.5pt -- (0,3.5);
\draw[name path=curve,red] plot[samples=100,domain=0:3,variable=\t]
({1+cos(deg(\w* \t)) * 5},{5+- sin(deg(\w\t))  \w* 5});
\drawname path=vline--+(90:3);
\path[name intersections={of=curve and vline, by=x0}];
\fill (x0) circle(1pt);
\path [draw,blue,
    name path=section,
    intersection segments={
        of=curve and vline,
        sequence = {L2},
    },
    postaction={tangent at=0}
    ];
\end{tikzpicture}
\end{document}

You can remove the draw, blue that is used just to visual see the effect of the sequence key... https://tikz.dev/pgfplots/libs-fillbetween#sec-46.6

Jasper Habicht · Accepted Answer · 2024-01-30T18:58:33.573

A more or less straight-forward idea would be to calculate two coordinates that are very close to the relevant coordinate on the plot trough which you want to draw a tangent and then draw a line through these two coordinates.

Since the plot in your example does not use a linear function, I added a reverse function to easier get the right values.

\documentclass[tikz, border=10pt]{standalone}
\usetikzlibrary{intersections, calc}
\begin{document}
\begin{tikzpicture}[
    >=latex,
    declare function={
        w = 0.7;
        curvex(\t) = 1+cos(deg(w\t))5;
        curvey(\t) = 5-sin(deg(w\t))w*5;
        reversex(\x) = rad(acos((\x-1)/5))/w;
    },
]
\draw[->, line width=0.5pt] (-0.3,0) -- (5.2,0);
\draw[->, line width=0.5pt] (0,-0.3) -- (0,3.5);
\draw[name path=curve, red] 
    plot[samples=100, smooth, domain=0:3, variable=\t] 
    ({curvex(\t)},{curvey(\t)});
\draw[name path=vline] (3,0) -- +(90:3);
\path[name intersections={of=curve and vline, by=x0}];

\fill (x0) circle[radius=1pt];
\pgfmathsetmacro{\i}{reversex(3)}
\coordinate (x1) at ({curvex(\i-0.01)},{curvey(\i-0.01)});
\coordinate (x2) at ({curvex(\i+0.01)},{curvey(\i+0.01)});
\draw[green] ($(x1)!-2cm!(x2)$) -- ($(x1)!2cm!(x2)$);
\end{tikzpicture}
\end{document}

That's great, it is new for me! – Hariz Khaled Jan 30 '24 at 20:45 — Hariz Khaled, Jan 30 '24 at 20:45

Draw tangent line on a curve

2 Answers2