iPad上的ab三角函数公式-垂直下落

几何画板及绘图内容加载中，请稍等……

2017-10-08 03:55

所属专题 Math Year 4 Unit 1

①本范例演示在iPad上通过GeoGebra演示三角函数与积分计算中，物体垂直下落的动态图形现象；②涉及的核心数学概念包括向量、三角函数、积分计算与最值优化；③作图要点提炼自构造摘要，使用了Intersect（相交）、AttachCopyToView（附加复制到视图）、r、hcfw、trev、hzcrto、wtr、ratecrt、Hcfw2wtr、Rateang、Haddon、Htotal、T2fall、Hzdvr、f、A、stroke1等GeoGebra命令与对象；④适合高中及以上数学学习，用于理解积分、向量与三角函数在物理现象中的应用。

GeoGebra 命令及参数

Intersect(Hzdvr, f, (9.81094355745193, -8.463856136758254)) → A
AttachCopyToView(PolyLine[(-8.00740462480568, -15.4988689005249), (NaN, NaN), (-8.00740462480568, -15.4988689005249), (-7.05718830814641, -15.18994967691), (-6.10697199148714, -15.18994967691), (-4.998386288718, -15.18994967691), (-4.04816997205873, -15.0354900651026), (-3.25632304150934, -14.7265708414877), (-2.78121488317971, -14.4176516178728), (-2.30610672485007, -13.9542727824505), (-2.14773733874019, -13.4908939470282), (-2.30610672485007, -12.4096766643761), (-2.62284549706983, -11.9462978289537), (-3.41469242761922, -11.328459381724), (-4.20653935816861, -11.328459381724), (-4.84001690260812, -11.9462978289537), (-4.84001690260812, -12.718595887991), (-4.68164751649824, -13.1819747234133), (-4.52327813038836, -13.6453535588356), (-4.36490874427848, -14.1087323942579), (-4.04816997205873, -14.5721112296803), (-3.88980058594885, -15.18994967691), (-3.73143119983897, -15.8077881241398), (-3.41469242761922, -16.7345457949845), (-3.25632304150934, -17.1979246304068), (-3.09795365539946, -17.8157630776366), (-3.09795365539946, -18.4336015248663), (-2.93958426928958, -19.0514399720961), (-2.93958426928958, -19.8237380311333), (-2.93958426928958, -20.4415764783631), (-3.09795365539946, -21.0594149255929), (-3.5730618137291, -21.5227937610152), (-4.36490874427848, -21.9861725964375), (-4.998386288718, -22.140632208245), (-5.63186383315751, -22.140632208245), (-6.26534137759702, -21.9861725964375), (-6.74044953592666, -21.6772533728226), (-7.05718830814641, -20.9049553137854), (-7.21555769425629, -20.4415764783631), (-7.05718830814641, -19.9781976429408), (-6.58208014981678, -19.6692784193259), (-5.31512506093775, -19.9781976429408), (-4.84001690260812, -20.1326572547482), (-4.20653935816861, -20.4415764783631), (-3.73143119983897, -20.750495701978), (-3.09795365539946, -21.0594149255929), (-2.46447611095995, -21.2138745374003), (-1.98936795263031, -21.3683341492078), (-1.19752102208092, -21.5227937610152), (-0.564043477641411, -21.6772533728226), (0.386172839017858, -21.6772533728226), (0.861280997347492, -21.0594149255929), (0.861280997347492, -20.1326572547482), (0.861280997347492, -19.2058995839036), (0.702911611237616, -18.7425207484812), (0.544542225127737, -18.2791419130589), (0.544542225127737, -18.8969803602887), (0.861280997347492, -19.6692784193259), (1.33638915567713, -20.5960360901705), (1.96986670011664, -21.0594149255929), (2.76171363066603, -21.2138745374003), (3.55356056121542, -21.0594149255929), (4.02866871954506, -20.4415764783631), (4.18703810565493, -19.6692784193259), (4.66214626398457, -19.2058995839036), (5.1372544223142, -19.360359195711), (5.45399319453396, -19.8237380311333), (5.77073196675372, -20.2871168665557), (6.24584012508335, -20.9049553137854), (6.72094828341298, -20.750495701978), (6.72094828341298, -19.9781976429408), (6.87931766952286, -19.5148188075184), (7.19605644174262, -19.0514399720961), (7.82953398618213, -19.360359195711), (8.14627275840188, -19.8237380311333), (8.46301153062164, -20.4415764783631), (8.93811968895127, -21.0594149255929), (9.57159723339079, -21.2138745374003), (10.0467053917204, -21.0594149255929), (10.3634441639402, -20.4415764783631), (10.5218135500501, -19.9781976429408), (10.6801829361599, -19.5148188075184), (10.8385523222698, -19.0514399720961), (11.3136604805994, -18.7425207484812), (10.6801829361599, -19.2058995839036), (10.6801829361599, -19.9781976429408), (11.3136604805994, -20.750495701978), (11.7887686389291, -21.0594149255929), (12.4222461833686, -21.3683341492078), (13.0557237278081, -21.5227937610152), (13.5308318861377, -21.6772533728226), (14.0059400444674, -21.2138745374003), (14.0059400444674, -20.5960360901705), (13.8475706583575, -19.8237380311333), (13.3724625000279, -18.8969803602887), (12.8973543416982, -17.970222689444), (12.1055074111488, -16.8890054067919), (11.3136604805994, -16.1167073477547), (10.8385523222698, -15.3444092887175), (10.3634441639402, -14.8810304532952), (10.2050747778303, -15.3444092887175), (10.3634441639402, -15.9622477359473), (10.6801829361599, -16.580086183177), (10.9969217083797, -17.3523842422142), (11.4720298667093, -17.8157630776366), (11.947138025039, -18.4336015248663), (12.4222461833686, -19.0514399720961), (12.7389849555883, -19.5148188075184), (13.214093113918, -19.9781976429408), (13.8475706583575, -20.750495701978), (14.481048202797, -20.750495701978), (14.7977869750168, -20.2871168665557), (15.1145257472365, -19.5148188075184), (15.2728951333464, -18.8969803602887), (15.2728951333464, -18.2791419130589), (15.4312645194562, -18.7425207484812), (15.5896339055661, -19.360359195711), (16.0647420638958, -19.9781976429408), (16.3814808361155, -20.5960360901705), (17.014958380555, -21.0594149255929), (17.4900665388847, -21.2138745374003), (17.9651746972143, -21.3683341492078), (18.7570216277637, -21.2138745374003), (19.0737603999834, -20.5960360901705), (19.2321297860933, -20.1326572547482), (19.0737603999834, -19.2058995839036), (18.5986522416538, -18.5880611366738), (18.4402828555439, -19.360359195711), (18.5986522416538, -20.1326572547482), (19.0737603999834, -21.0594149255929), (19.8656073305328, -22.6040110436673), (20.3407154888625, -23.530768714512), (20.8158236471921, -24.6119859971641), (21.1325624194118, -25.3842840562013), (21.1325624194118, -26.1565821152385), (20.1823461027526, -25.5387436680087), (19.7072379444229, -25.0753648325864), (19.5488685583131, -24.6119859971641), (19.3904991722032, -23.8396879381268), (19.5488685583131, -23.0673898790896), (20.4990848749723, -23.0673898790896), (21.1325624194118, -23.0673898790896), (NaN, NaN), (1.81149731400676, -16.1167073477547), (NaN, NaN), (1.81149731400676, -16.1167073477547), true], 1, (-9.716456293234058, -25.54028325569991), (35.50557673188053, 62.15668388788925), (0, 693), (555, 0)) → stroke1

AI 绘图提示语参考

画一个物体从高处垂直下落的动态图形，展示其运动轨迹与积分计算。图形包含一个曲线表示物体的下落路径，以及一个垂直线段表示物体下落的方向。路径曲线从左上方开始，经过一个最高点后逐渐下降至右下方。整个图形以坐标系为背景，坐标轴标注清晰，曲线和线段颜色突出，展现物理现象中的向量、三角函数和积分应用。

以上提示语为根据原始绘图命令整理而来，仅供参考。