File:Tangent half-angle formula.svg

Summary[edit]

Illustration for article en:Tangent half-angle formula. Created by Gustavb using Euklides.

Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following license:

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue

	This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
	You are free: to share – to copy, distribute and transmit the work to remix – to adapt the work Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
	This licensing tag was added to this file as part of the GFDL licensing update.http://creativecommons.org/licenses/by-sa/3.0/CC BY-SA 3.0Creative Commons Attribution-Share Alike 3.0truetrue

Source[edit]

Tangent_half-angle_formula.euk[edit]

box(-1.6, -1.6, 1.6, 1.6, 2.5)
thickness(.8)

% Axis
X1 = point(-1.7, 0); X2 = point(1.6, 0)
Y1 = point(0, -1.7); Y2 = point(0, 1.6)
color(darkgray);
draw(segment(X1,X2), full, arrow)
draw(segment(Y1,Y2), full, arrow)
color(black);

O = point(0,0);  % origo

% Unit circle
A = point(-1,0); B = point(1,0)
C = circle(A, B)

% Angle
phi interactive(48, -3, -180, 180, "", right)
P = point(C, phi:) 

% Where A->P intersects the Y-axis
I = intersection(line(A,P), line(Y1,Y2)) 

% P projected on X-axis
D = projection(P,line(X1,X2));

draw(C);
draw(P); draw(O,P)
draw(A); draw(I)
mark(B,O,P, simple, .5)
mark(O,A,P, simple, .6)
mark(D,P,B, simple, .6)
thickness(1.3); draw(line(A,P))
thickness(1.0); draw(P,D,A); draw(P,D,B)

% Draw labels
draw("$(0, t)$",I,.1,140:)
draw("$(-1,0)$",A,.08,145:)
draw("$\varphi$",O,.3,20:)
draw("$\varphi/2$",A,.4,13:)
draw("$\varphi \over 2$",P,.35,-78:)
draw("$(\cos \varphi,\sin \varphi)$",P,.15,-12:)
draw("$y$",Y2,.1,-30:); draw("$x$",X2,.1,-130:)

Instructions[edit]

1. Create EPS
   

   $ euk2eps Tangent_half-angle_formula.euk

2. Outline fonts
   

   $ eps2eps -dNOCACHE Tangent_half-angle_formula.eps Tangent_half-angle_formula2.eps

3. Fix bounding box
   

   $ ps2epsi Tangent_half-angle_formula2.eps Tangent_half-angle_formula.eps

4. Convert to Sketch
   

   $ pstoedit -f sk Tangent_half-angle_formula.eps Tangent_half-angle_formula.sk

5. Convert to SVG
   

   $ skconvert Tangent_half-angle_formula.sk Tangent_half-angle_formula.svg

6. Fix Tangent_half-angle_formula.svg with Inkscape