File:Tangent half-angle formula.png

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

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:)

Instructions

 * 1) Create EPS  $ euk2eps Tangent_half-angle_formula.euk
 * 2) Render EPS to PNG  $ convert -density 250 Tangent_half-angle_formula.eps Tangent_half-angle_formula.png
 * 3) Optimize PNG  $ optipng -zc1-9 -zm1-9 -zs0-2 -f0-5 Tangent_half-angle_formula.png