Image:Tangent half-angle formula.svg

[edit] Summary

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

[edit] Licensing

I, the copyright holder of this work, have published or 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". Aragonés | العربية | Asturianu | Български | বাংলা | ইমার ঠার/বিষ্ণুপ্রিয়া মণিপুরী | Brezhoneg | Bosanski | Català | Cebuano | Česky | Dansk | Deutsch | Ελληνικά | English | Esperanto | Español | Eesti | Euskara | فارسی | Suomi | Français | Gaeilge | Galego | עברית | Hrvatski | Magyar | Bahasa Indonesia | Ido | Íslenska | Italiano | 日本語 | ქართული | ភាសាខ្មែរ | 한국어 | Kurdî / كوردی | Latina | Lëtzebuergesch | Lietuvių | Bahasa Melayu | Nnapulitano | Nederlands | ‪Norsk (nynorsk)‬ | ‪Norsk (bokmål)‬ | Occitan | Polski | Português | Română | Русский | Slovenčina | Slovenščina | Shqip | Српски / Srpski | Svenska | తెలుగు | ไทย | Türkçe | Українська | اردو | Tiếng Việt | Volapük | Yorùbá | ‪中文(中国大陆)‬ | ‪中文(台灣)‬ | +/-

[edit] Source

[edit] Tangent_half-angle_formula.euk

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:)

[edit] Instructions

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

• User:Gustavb/Gallery