Difference between revisions of "User:Jonjoseph"
(22 intermediate revisions by the same user not shown) | |||
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label("$T$",T,NE); | label("$T$",T,NE); | ||
label("$S$",S,NW); | label("$S$",S,NW); | ||
− | label("$Z$",Z, | + | label("$Z$",Z,E); |
label("$Y$",Y,SE); | label("$Y$",Y,SE); | ||
label("$U$",U,E); | label("$U$",U,E); | ||
Line 55: | Line 55: | ||
draw(X--Y); | draw(X--Y); | ||
+ | draw(Z--Y, dashed); | ||
draw(W--X, red); | draw(W--X, red); | ||
draw(X--Z, red); | draw(X--Z, red); | ||
− | draw( | + | draw(Z--U, red); |
+ | draw(Z--W,red); | ||
+ | draw(U--X, red); | ||
draw(S--T--U--V--cycle); | draw(S--T--U--V--cycle); | ||
draw(X--T); | draw(X--T); | ||
Line 63: | Line 66: | ||
draw(Y--U); | draw(Y--U); | ||
draw(Z--V,dashed); | draw(Z--V,dashed); | ||
− | draw(W--U,dashed); | + | draw(W--U,red); |
+ | </asy> | ||
+ | |||
+ | <asy> | ||
+ | unitsize(1 cm); | ||
+ | pair A, B, C; | ||
+ | A = (0, 0); | ||
+ | B = (2, 0); | ||
+ | C = (2, 1.5); | ||
+ | |||
+ | draw(A--B--C--cycle); | ||
+ | label("$A$", A, W); | ||
+ | label("$B$", B, E); | ||
+ | label("$C$", C, N); | ||
+ | label("$5$", (A+B)/2, S); | ||
+ | label("$6$", (B+C)/2, E); | ||
+ | label("$\theta$", A, NE); | ||
+ | </asy> | ||
+ | |||
+ | <asy> | ||
+ | unitsize(0.2 cm); | ||
+ | pair A, B, E, P; | ||
+ | A = (0,0); | ||
+ | B = (8,0); | ||
+ | E=(1,2); | ||
+ | P = (B + reflect(A,(1,2))*(B))/2; | ||
+ | draw((-10,0)--(10,0)); | ||
+ | draw(A+(-1,-2)--8*E, red); | ||
+ | draw(A--(0,25)); | ||
+ | draw(B+-1*(1,2)--(9, 2)+7*(1,2), red); | ||
+ | draw(B--P,dashed); | ||
+ | dot("$A$", A, SE); | ||
+ | dot("$B$", B, SE); | ||
+ | dot("$P$", P, N); | ||
+ | label("$8$", (A + B)/2, S); | ||
+ | </asy> | ||
+ | |||
+ | <asy> | ||
+ | size(125); | ||
+ | real ticklen=3; | ||
+ | real tickspace=2; | ||
+ | |||
+ | real ticklength=0.1cm; | ||
+ | real axisarrowsize=0.14cm; | ||
+ | pen axispen=black+1.3bp; | ||
+ | real vectorarrowsize=0.2cm; | ||
+ | real tickdown=-0.5; | ||
+ | real tickdownlength=-0.15inch; | ||
+ | real tickdownbase=0.3; | ||
+ | real wholetickdown=tickdown; | ||
+ | void rr_cartesian_axes(real xleft, real xright, real ybottom, real ytop, real xstep=1, real ystep=1, bool useticks=false, bool complexplane=false, bool usegrid=true) { | ||
+ | import graph; | ||
+ | real i; | ||
+ | if(complexplane) { | ||
+ | label("$\textnormal{Re}$",(xright,0),SE); | ||
+ | label("$\textnormal{Im}$",(0,ytop),NW); | ||
+ | } else { | ||
+ | label("$x$",(xright+0.4,-0.5)); | ||
+ | label("$y$",(-0.5,ytop+0.2)); | ||
+ | } | ||
+ | |||
+ | ylimits(ybottom,ytop); | ||
+ | xlimits( xleft, xright); | ||
+ | real[] TicksArrx,TicksArry; | ||
+ | |||
+ | for(i=xleft+xstep; i<xright; i+=xstep) { | ||
+ | if(abs(i) >0.1) { | ||
+ | TicksArrx.push(i); | ||
+ | } | ||
+ | } | ||
+ | for(i=ybottom+ystep; i<ytop; i+=ystep) { | ||
+ | if(abs(i) >0.1) { | ||
+ | TicksArry.push(i); | ||
+ | } | ||
+ | } | ||
+ | |||
+ | if(usegrid) { | ||
+ | xaxis(BottomTop(extend=false), Ticks("%", TicksArrx ,pTick=gray(0.72),extend=true),p=invisible);//,above=true); | ||
+ | yaxis(LeftRight(extend=false),Ticks("%", TicksArry ,pTick=gray(0.72),extend=true), p=invisible);//,Arrows); | ||
+ | } | ||
+ | if(useticks) { | ||
+ | xequals(0, ymin=ybottom, ymax=ytop, p=axispen, Ticks("%",TicksArry , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize)); | ||
+ | yequals(0, xmin=xleft, xmax=xright, p=axispen, Ticks("%",TicksArrx , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize)); | ||
+ | |||
+ | } else { | ||
+ | xequals(0, ymin=ybottom, ymax=ytop, p=axispen, above=true, Arrows(size=axisarrowsize)); | ||
+ | yequals(0, xmin=xleft, xmax=xright, p=axispen, above=true, Arrows(size=axisarrowsize)); | ||
+ | } | ||
+ | }; | ||
+ | rr_cartesian_axes(-5,5,-1,10); | ||
+ | real f(real x) {return x*x;} | ||
+ | real g(real x) {return 2*x*x;} | ||
+ | draw(graph(f,-sqrt(10),sqrt(10),operator ..), red ,Arrows(size=axisarrowsize)); | ||
+ | draw(graph(g,-sqrt(5),sqrt(5),operator ..), blue ,Arrows(size=axisarrowsize)); | ||
+ | |||
+ | //dot((2,4), p=orange); | ||
+ | //dot((2,8),p=orange); | ||
+ | //draw((2,4)--(sqrt(2),4),p=orange, Arrow(size=2*axisarrowsize)); | ||
+ | draw((3,9)--(3/sqrt(2),9),p=black, Arrow(size=2*axisarrowsize)); | ||
+ | dot((3, 9), p=black); | ||
+ | |||
+ | //dot((-1,1), p=purple); | ||
+ | //dot((-1,2),p=purple); | ||
+ | //draw((-1,1)--(-1,2),p=purple, Arrow(size=2*axisarrowsize)); | ||
+ | </asy> | ||
+ | |||
+ | <asy> | ||
+ | size(170); | ||
+ | draw(circle((0,0),1)); | ||
+ | draw((0,0)--(1,0)--(1,.75)--cycle); | ||
+ | draw((0.9,0)--(0.9,0.1)--(1,0.1)); | ||
+ | label("$\theta$", (0.15,0), NE); | ||
+ | label("1", (0.5,0), S); | ||
+ | label("$\tan \theta$", (1,.375), E); | ||
+ | label("$\sec\theta$", (.5, .375), NW); | ||
+ | </asy> | ||
+ | |||
+ | <asy> | ||
+ | size(200); | ||
+ | import three; | ||
+ | currentprojection = orthographic(3.1, 2.1, 1); | ||
+ | triple A, B, X, Y, Z; | ||
+ | A = (1, 1, 0); | ||
+ | B = (0, 0, 1); | ||
+ | O = (0,0,0); | ||
+ | X = (1, 0, 0); | ||
+ | Y = (0, 1, 0); | ||
+ | Z = (0, 0, 1); | ||
+ | |||
+ | real big = 2; | ||
+ | |||
+ | draw(surface(-(big - 0.1)*X - (big - 0.1)*Y -- -(big - 0.1)*X + (big - 0.1)*Y -- (big - 0.1)*X + (big - 0.1)*Y -- (big - 0.1)*X - (big - 0.1)*Y--cycle), rgb(226, 253, 255), nolight); | ||
+ | draw(O--big*X, Arrow3(size = 0.2cm)); | ||
+ | draw(O-- -big*X, Arrow3(size = 0.2cm)); | ||
+ | draw(O-- big*Y, Arrow3(size = 0.2cm)); | ||
+ | draw(O-- -big*Y, Arrow3(size = 0.2cm)); | ||
+ | draw(O-- big*Z, Arrow3(size = 0.2cm)); | ||
+ | draw(O-- -big*Z, Arrow3(size = 0.2cm)); | ||
+ | |||
+ | label("$x$", big*X, NW); | ||
+ | label("$y$", big*Y, N); | ||
+ | label("$z$", big*Z, W); | ||
+ | |||
+ | draw(A--B, red, Arrow3(size = 0.3cm)); | ||
+ | |||
+ | dot("$A$", A, S); | ||
+ | dot("$B$", B, E); | ||
+ | </asy> | ||
+ | |||
+ | <asy> | ||
+ | import graph; | ||
+ | |||
+ | //size(6cm); | ||
+ | picture pic1; | ||
+ | real xsize=200, ysize=140; | ||
+ | size(pic1,xsize,ysize,IgnoreAspect); | ||
+ | |||
+ | real f(real x){return ((x - .5)^3 - .5 x + 1);} | ||
+ | xlimits(pic1, -2, 2); | ||
+ | ylimits(pic1, -2,2); | ||
+ | draw(pic1, graph(f,-1,2),black+1bp); | ||
+ | xaxis(pic1, Label("$x$",position=EndPoint, align=SE),Ticks("%"), Arrow); | ||
+ | yaxis(pic1, Label("$y$",position=EndPoint, align=NW),Ticks("%"), Arrow); | ||
+ | labelx(pic1, 1,2S); | ||
+ | labely(pic1, 1,2W); | ||
+ | label(pic1, "\scriptsize $y = g(x)$", (2.2,1)); | ||
+ | |||
+ | picture pic2; | ||
+ | size(pic2,xsize,ysize,IgnoreAspect); | ||
+ | |||
+ | real g(real x){return (3(x - .5)^2 - .5);} | ||
+ | xlimits(pic2, -2, 2); | ||
+ | ylimits(pic2, -2,2); | ||
+ | draw(pic2, graph(g,-0.5,1.5),black+1bp); | ||
+ | xaxis(pic2, Label("$x$",position=EndPoint, align=SE),Ticks("%"), Arrow); | ||
+ | yaxis(pic2, Label("$y$",position=EndPoint, align=NW),Ticks("%"), Arrow); | ||
+ | labelx(pic2, 1,2S); | ||
+ | labely(pic2, 1,2W); | ||
+ | label(pic2, "\scriptsize $y = g'(x)$", (2.2,1)); | ||
+ | |||
+ | picture pic3; | ||
+ | size(pic3,xsize,ysize,IgnoreAspect); | ||
+ | |||
+ | real h(real x){return (6(x - .5));} | ||
+ | xlimits(pic3, -2, 2); | ||
+ | ylimits(pic3, -2,2); | ||
+ | draw(pic3, graph(h,0.1,0.75),black+1bp); | ||
+ | xaxis(pic3, Label("$x$",position=EndPoint, align=SE),Ticks("%"), Arrow); | ||
+ | yaxis(pic3, Label("$y$",position=EndPoint, align=NW),Ticks("%"), Arrow); | ||
+ | labelx(pic3, 1,2S); | ||
+ | labely(pic3, 1,2W); | ||
+ | label(pic3, "\scriptsize $y = g''(x)$", (2.2,1)); | ||
+ | |||
+ | // Fit pic to W of origin: | ||
+ | // add(pic.fit(),(0,0),W); | ||
+ | |||
+ | real margin = 5mm; | ||
+ | add(pic1.fit(),(0,0), margin * N); | ||
+ | |||
+ | // Fit pic2 to E of (5mm,0): | ||
+ | add(pic2.fit(),(0,0), margin * S); | ||
+ | |||
+ | add(pic3.fit(), (0, 0), 12*margin*S); | ||
</asy> | </asy> |
Latest revision as of 21:43, 28 March 2022
Given a circle with center and a point
that lies outside the circle, bisect circle
with a second circle centered at
.
Problem from class: