unit cirlcle and sine

html('<h2>Sine and unit circle</h2> inspired by <a href="http://www.youtube.com/watch?v=Ohp6Okk_tww&feature=related">this video</a>' ) # http://www.sagemath.org/doc/reference/sage/plot/plot.html radius = 100 # scale for radius of "unit" circle graph_params = dict(xmin = -2*radius, xmax = 360, ymin = -(radius+30), ymax = radius+30, aspect_ratio=1, axes = False ) def sine_and_unit_circle( angle=30, instant_show = True, show_pi=True ): ccenter_x, ccenter_y = -radius, 0 # center of cirlce on real coords sine_x = angle # the big magic to sync both graphs :) current_y = circle_y = sine_y = radius * sin(angle*pi/180) circle_x = ccenter_x + radius * cos(angle*pi/180) graph = Graphics() # we'll put unit circle and sine function on the same graph # so there will be some coordinate mangling ;) # CIRCLE unit_circle = circle((ccenter_x, ccenter_y), radius, color="#ccc") # SINE x = var('x') sine = plot( radius * sin(x*pi/180) , (x, 0, 360), color="#ccc" ) graph += unit_circle + sine # CIRCLE axis # x axis graph += arrow( [-2*radius, 0], [0, 0], color = "#666" ) graph += text("$(1, 0)$", [-16, 16], color = "#666") # circle y axis graph += arrow( [ccenter_x,-radius], [ccenter_x, radius], color = "#666" ) graph += text("$(0, 1)$", [ccenter_x, radius+15], color = "#666") # circle center graph += text("$(0, 0)$", [ccenter_x, 0], color = "#666") # SINE x axis graph += arrow( [0,0], [360, 0], color = "#000" ) # let's set tics # or http://aghitza.org/posts/tweak_labels_and_ticks_in_2d_plots_using_matplotlib/ # or wayt for http://trac.sagemath.org/sage_trac/ticket/1431 # ['$-\pi/3$', '$2\pi/3$', '$5\pi/3$'] for x in range(0, 361, 30): graph += point( [x, 0] ) angle_label = ". $%3d^{\circ}$ " % x if show_pi: angle_label += " $(%s\pi) $"% x/180 graph += text(angle_label, [x, 0], rotation=-90, vertical_alignment='top', fontsize=8, color="#000" ) # CURRENT VALUES # SINE -- y graph += arrow( [sine_x,0], [sine_x, sine_y], width=1, arrowsize=3) graph += arrow( [circle_x,0], [circle_x, circle_y], width=1, arrowsize=3) graph += line(([circle_x, current_y], [sine_x, current_y]), rgbcolor="#0F0", linestyle = "--", alpha=0.5) # LABEL on sine graph += text("$(%d^{\circ}, %3.2f)$"%(sine_x, float(current_y)/radius), [sine_x+30, current_y], color = "#0A0") # ANGLE -- x # on sine graph += arrow( [0,0], [sine_x, 0], width=1, arrowsize=1, color='red') # on circle graph += disk( (ccenter_x, ccenter_y), float(radius)/4, (0, angle*pi/180), color='red', fill=False, thickness=1) graph += arrow( [ccenter_x, ccenter_y], [circle_x, circle_y], rgbcolor="#cccccc", width=1, arrowsize=1) if instant_show: show (graph, **graph_params) return graph ##################### # make Interaction ###################### @interact def _( angle = slider([0..360], default=30, step_size=5, label="Pasirinkite kampą: ", display_value=True) ): sine_and_unit_circle(angle, show_pi = False) 

animate( [sine_and_unit_circle(angle, show_pi = False, instant_show=False) for angle in range(0, 361, 15) ] , **graph_params ).show( delay=50 ) # delay makes pauses between frames (now it's half second)