正弦定律 - 导航应用
几何画板及绘图内容加载中,请稍等……
这个范例演示了正弦定律在导航中的应用。核心数学概念包括正弦定律及其在解决三角形问题中的应用。通过构造摘要中的命令,如Segment, Angle, AttachCopyToView等,可以构建一个三角形并应用正弦定律。适合高中数学教学和学习。
GeoGebra 命令及参数
Segment(A, B) → cSegment(C, A) → bSegment(B, C) → aAngle(C, A, B) → CABAngle(B, C, A) → BCAAngle(A, B, C) → ABCAttachCopyToView(PolyLine[(6.879999999999999, 1.219999999999997), (6.819999999999999, 1.179999999999997), (6.679999999999999, 1.179999999999997), (6.539999999999999, 1.159999999999997), (6.419999999999999, 1.159999999999997), (6.339999999999999, 1.159999999999997), (6.239999999999999, 1.159999999999997), (6.079999999999999, 1.119999999999997), (5.999999999999999, 1.119999999999997), (5.9399999999999995, 1.099999999999997), (5.779999999999999, 1.059999999999997), (5.679999999999999, 1.039999999999997), (5.599999999999999, 1.019999999999997), (5.539999999999999, 0.999999999999997), (5.459999999999999, 0.979999999999997), (5.3999999999999995, 0.939999999999997), (5.319999999999999, 0.8999999999999969), (5.259999999999999, 0.8799999999999969), (5.159999999999999, 0.8199999999999968), (5.059999999999999, 0.7399999999999969), (4.939999999999999, 0.6799999999999968), (4.8599999999999985, 0.6199999999999968), (4.8199999999999985, 0.5599999999999968), (4.8199999999999985, 0.47999999999999676), (4.839999999999999, 0.37999999999999673), (4.939999999999999, 0.3399999999999967), (5.059999999999999, 0.2799999999999967), (5.159999999999999, 0.2399999999999967), (5.259999999999999, 0.19999999999999665), (5.379999999999999, 0.17999999999999666), (5.499999999999999, 0.13999999999999663), (5.599999999999999, 0.09999999999999662), (5.699999999999999, 0.07999999999999662), (5.819999999999999, 0.05999999999999661), (5.959999999999999, 0.0399999999999966), (6.079999999999999, 0.019999999999996597), (6.219999999999999, -3.4106051316484823E-15), (6.359999999999999, -3.4106051316484823E-15), (6.499999999999999, -3.4106051316484823E-15), (6.619999999999999, -3.4106051316484823E-15), (6.699999999999999, -3.4106051316484823E-15), (6.8599999999999985, -3.4106051316484823E-15), (6.959999999999999, -3.4106051316484823E-15), (7.059999999999999, 0.019999999999996597), (7.139999999999999, 0.0399999999999966), (7.199999999999999, 0.05999999999999661), (7.259999999999999, 0.07999999999999662), (7.339999999999999, 0.09999999999999662), (7.459999999999999, 0.19999999999999665), (7.579999999999999, 0.2799999999999967), (7.639999999999999, 0.3599999999999967), (7.659999999999999, 0.41999999999999676), (7.679999999999999, 0.4999999999999968), (7.679999999999999, 0.6399999999999968), (7.659999999999999, 0.7399999999999969), (7.639999999999999, 0.7999999999999969), (7.599999999999999, 0.9199999999999969), (7.499999999999999, 0.999999999999997), (7.439999999999999, 1.039999999999997), (7.379999999999999, 1.079999999999997), (7.3199999999999985, 1.119999999999997), (7.219999999999999, 1.139999999999997), (7.139999999999999, 1.159999999999997), (7.019999999999999, 1.179999999999997), (6.899999999999999, 1.179999999999997), (6.799999999999999, 1.179999999999997), (6.699999999999999, 1.179999999999997), (6.639999999999999, 1.159999999999997), (6.579999999999999, 1.099999999999997), (6.519999999999999, 1.079999999999997), (NaN, NaN), (5.3999999999999995, 4.2799999999999985), (5.319999999999999, 4.3199999999999985), (5.159999999999999, 4.3199999999999985), (5.039999999999998, 4.339999999999998), (4.839999999999999, 4.3599999999999985), (4.719999999999999, 4.399999999999999), (4.579999999999998, 4.439999999999999), (4.459999999999999, 4.479999999999999), (4.339999999999999, 4.539999999999998), (4.119999999999999, 4.599999999999998), (3.9599999999999986, 4.619999999999998), (3.759999999999999, 4.619999999999998), (3.5599999999999987, 4.619999999999998), (3.359999999999999, 4.599999999999998), (3.159999999999999, 4.579999999999998), (2.979999999999999, 4.579999999999998), (2.779999999999999, 4.579999999999998), (2.579999999999999, 4.579999999999998), (2.339999999999999, 4.579999999999998), (2.1399999999999992, 4.579999999999998), (1.919999999999999, 4.579999999999998), (1.699999999999999, 4.579999999999998), (1.5199999999999991, 4.619999999999998), (1.3799999999999992, 4.679999999999998), (1.2199999999999993, 4.719999999999998), (1.1199999999999992, 4.759999999999998), (1.0399999999999994, 4.759999999999998), (0.9399999999999993, 4.759999999999998), (0.8199999999999993, 4.759999999999998), (0.7199999999999993, 4.719999999999998), (0.5999999999999993, 4.659999999999998), (0.47999999999999937, 4.579999999999998), (0.2999999999999994, 4.499999999999998), (0.1399999999999994, 4.459999999999998), (-0.06000000000000056, 4.439999999999999), (-0.24000000000000052, 4.439999999999999), (-0.4400000000000005, 4.439999999999999), (-0.6600000000000005, 4.439999999999999), (-0.9000000000000005, 4.459999999999998), (-1.1200000000000003, 4.479999999999999), (-1.3400000000000003, 4.479999999999999), (-1.5400000000000003, 4.479999999999999), (-1.7200000000000002, 4.479999999999999), (-1.9000000000000004, 4.479999999999999), (-2.04, 4.459999999999998), (-2.18, 4.459999999999998), (-2.3200000000000003, 4.459999999999998), (-2.4600000000000004, 4.439999999999999), (-2.62, 4.399999999999999), (-2.74, 4.339999999999998), (-2.8800000000000003, 4.2799999999999985), (-3, 4.219999999999998), (-3.08, 4.159999999999998), (-3.14, 4.099999999999998), (-3.18, 4.039999999999998), (-3.24, 3.979999999999998), (-3.3000000000000003, 3.919999999999998), (-3.36, 3.899999999999998), (-3.44, 3.839999999999998), (-3.56, 3.779999999999998), (-3.66, 3.719999999999998), (NaN, NaN), (5.259999999999999, 4.419999999999998), (5.4799999999999995, 4.379999999999998), (6.339999999999999, 3.819999999999998), (NaN, NaN), (5.359999999999999, 4.419999999999998), (6.039999999999999, 4.239999999999998), (6.099999999999999, 4.199999999999998), (6.159999999999999, 4.139999999999998), (6.199999999999999, 4.079999999999998), (6.279999999999999, 4.019999999999998), (NaN, NaN), (6.279999999999999, 4.039999999999998), (6.299999999999999, 3.919999999999998), (6.359999999999999, 3.879999999999998), (6.419999999999999, 3.839999999999998), (6.479999999999999, 3.799999999999998), (6.519999999999999, 3.719999999999998), (6.579999999999999, 3.679999999999998), (6.619999999999999, 3.599999999999998), (NaN, NaN), (8.639999999999999, 3.219999999999998), (8.78, 3.179999999999998), (8.899999999999999, 3.159999999999998), (9.019999999999998, 3.139999999999998), (9.159999999999998, 3.139999999999998), (9.259999999999998, 3.139999999999998), (9.399999999999999, 3.159999999999998), (9.519999999999998, 3.219999999999998), (9.639999999999999, 3.2799999999999976), (9.739999999999998, 3.3599999999999977), (9.859999999999998, 3.4199999999999977), (9.959999999999999, 3.499999999999998), (10.04, 3.539999999999998), (10.179999999999998, 3.619999999999998), (10.279999999999998, 3.699999999999998), (10.379999999999999, 3.739999999999998), (10.479999999999999, 3.799999999999998), (10.559999999999999, 3.839999999999998), (10.699999999999998, 3.959999999999998), (10.759999999999998, 4.039999999999998), (10.819999999999999, 4.099999999999998), (10.879999999999999, 4.179999999999998), (10.979999999999999, 4.239999999999998), (11.079999999999998, 4.299999999999998), (11.239999999999998, 4.379999999999998), (11.359999999999998, 4.419999999999998), (11.479999999999999, 4.439999999999999), (11.599999999999998, 4.479999999999999), (11.679999999999998, 4.499999999999998), (11.779999999999998, 4.519999999999999), (11.879999999999999, 4.519999999999999), (11.959999999999997, 4.519999999999999), (12.039999999999997, 4.539999999999998), (12.139999999999999, 4.559999999999998), (12.259999999999998, 4.559999999999998), (12.379999999999997, 4.579999999999998), (12.499999999999998, 4.619999999999998), (12.599999999999998, 4.619999999999998), (12.739999999999998, 4.679999999999998), (12.799999999999997, 4.699999999999998), (12.899999999999999, 4.719999999999998), (12.999999999999998, 4.719999999999998), true], 1, (-4.3, -5.120000000000005), (13.179999999999998, 6.399999999999999), (0, 576), (874, 0)) → stroke1AttachCopyToView(PolyLine[(-0.3400000000000005, 0.6799999999999968), (-0.3600000000000005, 0.7399999999999969), (-0.3200000000000005, 0.8399999999999969), (-0.2600000000000005, 0.939999999999997), (-0.20000000000000054, 1.019999999999997), (-0.14000000000000054, 1.099999999999997), (-0.10000000000000055, 1.159999999999997), (-0.06000000000000056, 1.219999999999997), (0.019999999999999428, 1.339999999999997), (0.05999999999999942, 1.399999999999997), (0.09999999999999942, 1.459999999999997), (0.1399999999999994, 1.5199999999999971), (0.1999999999999994, 1.5799999999999972), (0.2599999999999994, 1.6399999999999972), (0.3599999999999994, 1.7399999999999973), (0.4199999999999994, 1.7999999999999972), (0.47999999999999937, 1.8599999999999972), (0.5599999999999994, 1.8799999999999972), (0.6199999999999993, 1.8999999999999972), (0.7599999999999993, 1.8999999999999972), (0.8399999999999993, 1.8999999999999972), (0.9199999999999993, 1.8799999999999972), (0.9799999999999993, 1.8199999999999972), (1.0599999999999992, 1.7999999999999972), (1.1199999999999992, 1.7599999999999973), (1.1799999999999993, 1.6999999999999973), (1.2399999999999993, 1.6599999999999973), (1.2999999999999992, 1.6399999999999972), (1.3599999999999992, 1.6199999999999972), (1.4599999999999993, 1.6199999999999972), (1.5799999999999992, 1.6199999999999972), (1.6799999999999993, 1.6199999999999972), (1.739999999999999, 1.5999999999999972), (1.8399999999999992, 1.5599999999999972), (1.8999999999999992, 1.5399999999999971), (1.939999999999999, 1.419999999999997), (1.939999999999999, 1.339999999999997), (1.939999999999999, 1.2599999999999971), (1.939999999999999, 1.159999999999997), (1.939999999999999, 1.079999999999997), (1.939999999999999, 0.959999999999997), (1.939999999999999, 0.8799999999999969), (1.939999999999999, 0.7799999999999969), (1.939999999999999, 0.6999999999999968), (1.8399999999999992, 0.6999999999999968), (1.699999999999999, 0.6799999999999968), (1.5599999999999992, 0.6599999999999968), (1.4199999999999993, 0.6399999999999968), (1.2799999999999991, 0.6199999999999968), (1.1599999999999993, 0.6199999999999968), (1.0599999999999992, 0.5999999999999968), (0.9599999999999993, 0.5999999999999968), (0.8599999999999993, 0.5999999999999968), (0.7199999999999993, 0.5999999999999968), (0.5799999999999993, 0.5999999999999968), (0.4399999999999994, 0.5999999999999968), (0.2999999999999994, 0.5999999999999968), (0.15999999999999942, 0.6199999999999968), (0.039999999999999425, 0.6399999999999968), (-0.08000000000000056, 0.6399999999999968), (-0.18000000000000055, 0.6399999999999968), (-0.2600000000000005, 0.6399999999999968), (-0.3400000000000005, 0.6399999999999968), (-0.4000000000000005, 0.6599999999999968), true], 1, (-4.3, -5.120000000000005), (13.179999999999998, 6.399999999999999), (0, 576), (874, 0)) → stroke2AttachCopyToView(PolyLine[(0.8199999999999993, 3.2799999999999976), (0.7399999999999993, 3.2999999999999976), (0.5999999999999993, 3.2599999999999976), (0.5399999999999994, 3.239999999999998), (0.47999999999999937, 3.219999999999998), (0.4199999999999994, 3.199999999999998), (0.3599999999999994, 3.179999999999998), (0.2799999999999994, 3.159999999999998), (0.2199999999999994, 3.139999999999998), (0.15999999999999942, 3.099999999999998), (0.09999999999999942, 3.079999999999998), (0.019999999999999428, 3.059999999999998), (-0.06000000000000056, 3.019999999999998), (-0.12000000000000055, 2.9799999999999978), (-0.20000000000000054, 2.9599999999999977), (-0.2600000000000005, 2.9199999999999977), (-0.3200000000000005, 2.8999999999999977), (-0.4000000000000005, 2.8599999999999977), (-0.4800000000000005, 2.8199999999999976), (-0.5600000000000005, 2.7599999999999976), (-0.6400000000000005, 2.6999999999999975), (-0.7200000000000004, 2.6399999999999975), (-0.8000000000000005, 2.5799999999999974), (-0.8800000000000004, 2.4799999999999973), (-0.9800000000000004, 2.3399999999999976), (-1.0400000000000005, 2.2999999999999976), (-1.0600000000000005, 2.2399999999999975), (-1.1000000000000003, 2.1799999999999975), (-1.1200000000000003, 2.1199999999999974), (-1.1600000000000004, 2.0399999999999974), (-1.2000000000000004, 1.9599999999999973), (-1.2400000000000004, 1.8999999999999972), (-1.2600000000000005, 1.8399999999999972), (-1.2800000000000005, 1.7799999999999971), (-1.3200000000000003, 1.6599999999999973), (-1.3400000000000003, 1.5799999999999972), (-1.3600000000000003, 1.5199999999999971), (-1.3800000000000003, 1.459999999999997), (-1.4000000000000004, 1.379999999999997), (-1.4200000000000004, 1.3199999999999972), (-1.4400000000000004, 1.2599999999999971), (-1.4600000000000004, 1.199999999999997), (-1.4800000000000004, 1.119999999999997), (-1.5000000000000004, 1.059999999999997), (-1.5200000000000002, 0.979999999999997), (-1.5600000000000003, 0.8799999999999969), (-1.5800000000000003, 0.7599999999999969), (-1.6000000000000003, 0.6799999999999968), (-1.6400000000000003, 0.5799999999999969), (-1.6600000000000004, 0.4999999999999968), (-1.6800000000000004, 0.39999999999999675), (-1.7000000000000004, 0.2999999999999967), (-1.7400000000000002, 0.19999999999999665), (-1.7400000000000002, 0.09999999999999662), (-1.7800000000000002, 0.019999999999996597), (-1.8000000000000003, -0.08000000000000344), (-1.8200000000000003, -0.14000000000000346), (-1.8400000000000003, -0.2400000000000035), (-1.8800000000000003, -0.36000000000000354), (-1.9400000000000002, -0.6000000000000036), (-1.9600000000000002, -0.6800000000000037), (-1.9800000000000002, -0.7600000000000037), (-2.0200000000000005, -0.9000000000000038), (-2.04, -0.9600000000000037), (-2.04, -1.0400000000000038), (-2.06, -1.1000000000000039), (-2.08, -1.160000000000004), (-2.12, -1.3000000000000038), (-2.14, -1.400000000000004), (-2.16, -1.480000000000004), (-2.16, -1.600000000000004), (-2.16, -1.680000000000004), (-2.16, -1.800000000000004), (-2.16, -1.9400000000000042), (-2.16, -2.040000000000004), (-2.16, -2.140000000000004), (-2.14, -2.240000000000004), (-2.12, -2.3000000000000043), (-2.1, -2.3600000000000043), (-2.08, -2.4800000000000044), (-2.0200000000000005, -2.5800000000000045), (-1.9600000000000002, -2.6400000000000046), (-1.9400000000000002, -2.7000000000000046), (-1.8800000000000003, -2.740000000000004), (-1.8200000000000003, -2.8200000000000043), (-1.7600000000000002, -2.8600000000000043), (-1.7000000000000004, -2.9000000000000044), (-1.6400000000000003, -2.9600000000000044), (-1.5800000000000003, -3.0000000000000044), (-1.5200000000000002, -3.0400000000000045), (-1.4400000000000004, -3.0600000000000045), (-1.3800000000000003, -3.1000000000000045), (-1.3000000000000003, -3.1000000000000045), (-1.2400000000000004, -3.1400000000000046), (-1.1600000000000004, -3.1600000000000046), (-1.0800000000000003, -3.1600000000000046), (-1.0200000000000005, -3.1800000000000046), (-0.9600000000000004, -3.2000000000000046), (-0.8600000000000004, -3.2200000000000046), (-0.7800000000000005, -3.2200000000000046), (-0.7000000000000005, -3.2400000000000047), (-0.6200000000000004, -3.2400000000000047), (-0.5200000000000005, -3.2600000000000047), (-0.4400000000000005, -3.2600000000000047), (-0.3600000000000005, -3.2600000000000047), true], 1, (-4.3, -5.120000000000005), (13.179999999999998, 6.399999999999999), (0, 576), (874, 0)) → stroke3
AI 绘图提示语参考
绘制一个三角形,分别标记为A、B、C,然后测量角A、B、C的大小。接着,画出三角形的边AB、BC、CA,并在三角形内部绘制一条曲线,模拟航行应用中使用正弦定律解决三角形问题的过程。
以上提示语为根据原始绘图命令整理而来,仅供参考。