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A want to add the inverse trig.function for tangens to the code of asymptote. Thank you for adivise.

settings.outformat="pdf";
unitsize(2.5cm);
import graph;
     
real xmin = -pi/2;
real xmax = pi/2;
real ymin = -pi/2;
real ymax = pi/2;

xlimits(xmin,xmax);
ylimits(ymin,ymax);

//axis and the grid :

xaxis(Label("$x$",align=2E),Ticks("$%.2f$",new real[]{xmin,-1,1,xmax},Size=1mm,1bp),Arrow);
yaxis(Label("$y$",align=2N),Ticks("$%.2f$",new real[]{xmin,-1,1,xmax},Size=1mm,1bp),Arrow);

// function y=sin(x)
    real f(real x) {return sin(x)/cos(x); }
    path g = graph(f,xmin+0.5, xmax-0.5);
    draw(g,red,
        L= Label("$y=tan(x)$", UnFill,          
        position=EndPoint));
    
// function y=x
    draw((xmin-0.25,ymin-0.25)--(xmax+0.25,ymax+0.25),
        L= Label("$y=x$", UnFill,position=EndPoint));

Image of trigonometric cotg and its inverse arccotg functions

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6
  • 1
    What is your desired image?
    – user213378
    Commented Oct 13, 2020 at 14:34
  • 1
    atan for arctangent in radians, aTan for degrees. See asymptote.sourceforge.io/doc/…. You can compute arccotan from arctan.
    – Charles Staats
    Commented Oct 13, 2020 at 16:49
  • 1
    Please edit your original post. Don't post updates as answers.
    – Teepeemm
    Commented Oct 14, 2020 at 12:46
  • Welcome to TeX.SE!
    – Zarko
    Commented Oct 14, 2020 at 14:33
  • The graph and its inverse are symmetric to the bisector y=x, so one way is rotate it to x-axis, reflex to y-axis, then rotate back, and we get the graph of the inverse. This way rotate(45)*yscale(-1)*rotate(-45) works for any curve. // http://asymptote.ualberta.ca/ unitsize(1cm); import graph; import math; axes("$x$","$y$"); drawline((0,0),(1,1),gray+.3pt); real dx=.35; path g = graph(tan,-pi/2+dx, pi/2-dx); draw(g,red); draw(rotate(45)*yscale(-1)*rotate(-45)*g,blue);
    – Black Mild
    Commented Jan 29, 2021 at 15:04

1 Answer 1

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1

The general idea for drawing an inverse is to plot (f(x),x) in some manner. With the cotangent of your image, that would mean changing your code to

real xmin = 0;
real xmax = pi;
real ymin = -pi/2;
real ymax = pi/2;
...
real f(real x) {return cos(x)/sin(x); }

and then adding at the end:

pair h(real t) { return (f(t),t); }
path j = graph(h,xmin+0.3,xmax-0.3);
draw(j,blue,L=Label("$y=cotg^{-1}(x)$", UnFill,
    position=EndPoint));

Resulting in:

output

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