Difference between revisions of "User:Jonjoseph"
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</asy> | </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> | <asy> | ||
Line 155: | Line 170: | ||
//dot((-1,2),p=purple); | //dot((-1,2),p=purple); | ||
//draw((-1,1)--(-1,2),p=purple, Arrow(size=2*axisarrowsize)); | //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: