| [00:00.00] | 作曲 : 天儿 |
| [00:01.00] | 作词 : 天儿 |
| [00:10.56] | when you first study math about 1234 |
| [00:12.88] | first study equation about xyzt |
| [00:14.94] | It will help you to think in a logical way |
| [00:16.96] | When you sing sine,cosine,cosine,tangent |
| [00:19.28] | Sine,cosine,tangent,cotangent |
| [00:21.40] | Sine,cosine,..,secant,cosecant |
| [00:23.57] | Let's sing a song about trig-functions |
| [00:25.82] | sin（2π+α）=sinα |
| [00:27.94] | cos（2π+α）=cosα |
| [00:29.89] | tan（2π+α）=tanα |
| [00:31.83] | which is induction formula1,and induction formula 2 |
| [00:34.23] | sin（π+α）= —sinα |
| [00:36.35] | cos（π+α）=—cosα |
| [00:38.63] | tan（π+α）= tanα |
| [00:40.69] | sin（π－α）= sinα |
| [00:42.53] | cos（π－α）=－cosα |
| [00:44.99] | tan（π－α）=－tanα |
| [00:47.11] | These are all those "name donot -change" |
| [00:49.29] | As pi goes to half pi the difference shall be huge |
| [00:51.36] | sin（π/2+α）=cosα |
| [00:53.48] | sin（π/2－α）=cosα |
| [00:55.45] | cos（π/2+α）=－sinα |
| [00:57.84] | cos（π/2－α）=sinα |
| [00:59.92] | tan（π/2+α）=－cotα |
| [01:01.77] | tan（π/2－α）=cotα |
| [01:08.60] | That is to say the odds will change,evens are conserved |
| [01:13.47] | The notations that they get depend on where they are |
| [01:17.08] | But no matter where you are |
| [01:19.16] | I‘ve gotta say that |
| [01:21.49] | If you were sine curve,I'd be your cosine curve |
| [01:25.73] | I'll be your derivative,you'll be my negtive one |
| [01:29.76] | As you change you amplitude,I change my phase |
| [01:34.17] | We can oscillate freely in the external space |
| [01:38.44] | As we change our period and costant at hand |
| [01:42.61] | We travel from the origin to infinity |
| [01:46.85] | It's you sine,and you cosine |
| [01:51.27] | Who make charming music around the world |
| [01:55.45] | It's you tangent,cotangent |
| [01:59.74] | Who proclaim the true meaning of centrosymmetry |
| [02:03.44] | B BOX |
| [02:46.93] | You wanna measure width of a river,height of a tower |
| [02:49.27] | You scratch your head which cost you more than an hour |
| [02:51.40] | You don't need to ask any "gods" or" master" for help |
| [02:53.49] | This group of formulas are gonna help you solve |
| [02:55.82] | sin(α+β)=sinα•cosβ+cosα•sinβ |
| [02:58.94] | cos(α+β)=cosα•cosβ-sinα•sinβ |
| [03:02.22] | tan(α+β)=(tanα+tanβ)/(1-tanα•tanβ) |
| [03:06.25] | sin(α-β)=sinα•cosβ-cosα•sinβ |
| [03:09.59] | cos(α-β)=cosα•cosβ+sinα•sinβ |
| [03:12.93] | tan(α-β)=(tanα-tanβ)/(1+tanα•tanβ) |
| [03:17.99] | As you come across a right triangle you fell easy to sovle |
| [03:20.23] | But an obtuse triange's gonna make you feel confused |
| [03:22.26] | Don't worry about what you do |
| [03:23.64] | There are always means to solve |
| [03:24.80] | As long as you master the sine cosine law |
| [03:30.04] | At this momnet I've got nothing to say |
| [03:33.80] | As trig-functions rain down upon me |
| [03:38.45] | At this momnet I've got nothing to say |
| [03:42.52] | Let's sing a song about trig-functios |
| [03:47.13] | Long live the trigonometric functions |
| [03:55.85] |
| [00:00.00] | zuo qu : tian r |
| [00:01.00] | zuo ci : tian r |
| [00:10.56] | when you first study math about 1234 |
| [00:12.88] | first study equation about xyzt |
| [00:14.94] | It will help you to think in a logical way |
| [00:16.96] | When you sing sine, cosine, cosine, tangent |
| [00:19.28] | Sine, cosine, tangent, cotangent |
| [00:21.40] | Sine, cosine,.., secant, cosecant |
| [00:23.57] | Let' s sing a song about trigfunctions |
| [00:25.82] | sin 2 sin |
| [00:27.94] | cos 2 cos |
| [00:29.89] | tan 2 tan |
| [00:31.83] | which is induction formula1, and induction formula 2 |
| [00:34.23] | sin sin |
| [00:36.35] | cos cos |
| [00:38.63] | tan tan |
| [00:40.69] | sin sin |
| [00:42.53] | cos cos |
| [00:44.99] | tan tan |
| [00:47.11] | These are all those " name donot change" |
| [00:49.29] | As pi goes to half pi the difference shall be huge |
| [00:51.36] | sin 2 cos |
| [00:53.48] | sin 2 cos |
| [00:55.45] | cos 2 sin |
| [00:57.84] | cos 2 sin |
| [00:59.92] | tan 2 cot |
| [01:01.77] | tan 2 cot |
| [01:08.60] | That is to say the odds will change, evens are conserved |
| [01:13.47] | The notations that they get depend on where they are |
| [01:17.08] | But no matter where you are |
| [01:19.16] | I' ve gotta say that |
| [01:21.49] | If you were sine curve, I' d be your cosine curve |
| [01:25.73] | I' ll be your derivative, you' ll be my negtive one |
| [01:29.76] | As you change you amplitude, I change my phase |
| [01:34.17] | We can oscillate freely in the external space |
| [01:38.44] | As we change our period and costant at hand |
| [01:42.61] | We travel from the origin to infinity |
| [01:46.85] | It' s you sine, and you cosine |
| [01:51.27] | Who make charming music around the world |
| [01:55.45] | It' s you tangent, cotangent |
| [01:59.74] | Who proclaim the true meaning of centrosymmetry |
| [02:03.44] | B BOX |
| [02:46.93] | You wanna measure width of a river, height of a tower |
| [02:49.27] | You scratch your head which cost you more than an hour |
| [02:51.40] | You don' t need to ask any " gods" or" master" for help |
| [02:53.49] | This group of formulas are gonna help you solve |
| [02:55.82] | sin sin cos cos sin |
| [02:58.94] | cos cos cos sin sin |
| [03:02.22] | tan tan tan 1tan tan |
| [03:06.25] | sin sin cos cos sin |
| [03:09.59] | cos cos cos sin sin |
| [03:12.93] | tan tan tan 1 tan tan |
| [03:17.99] | As you come across a right triangle you fell easy to sovle |
| [03:20.23] | But an obtuse triange' s gonna make you feel confused |
| [03:22.26] | Don' t worry about what you do |
| [03:23.64] | There are always means to solve |
| [03:24.80] | As long as you master the sine cosine law |
| [03:30.04] | At this momnet I' ve got nothing to say |
| [03:33.80] | As trigfunctions rain down upon me |
| [03:38.45] | At this momnet I' ve got nothing to say |
| [03:42.52] | Let' s sing a song about trigfunctios |
| [03:47.13] | Long live the trigonometric functions |
| [03:55.85] |
| [00:00.00] | zuò qǔ : tiān r |
| [00:01.00] | zuò cí : tiān r |
| [00:10.56] | when you first study math about 1234 |
| [00:12.88] | first study equation about xyzt |
| [00:14.94] | It will help you to think in a logical way |
| [00:16.96] | When you sing sine, cosine, cosine, tangent |
| [00:19.28] | Sine, cosine, tangent, cotangent |
| [00:21.40] | Sine, cosine,.., secant, cosecant |
| [00:23.57] | Let' s sing a song about trigfunctions |
| [00:25.82] | sin 2 sin |
| [00:27.94] | cos 2 cos |
| [00:29.89] | tan 2 tan |
| [00:31.83] | which is induction formula1, and induction formula 2 |
| [00:34.23] | sin sin |
| [00:36.35] | cos cos |
| [00:38.63] | tan tan |
| [00:40.69] | sin sin |
| [00:42.53] | cos cos |
| [00:44.99] | tan tan |
| [00:47.11] | These are all those " name donot change" |
| [00:49.29] | As pi goes to half pi the difference shall be huge |
| [00:51.36] | sin 2 cos |
| [00:53.48] | sin 2 cos |
| [00:55.45] | cos 2 sin |
| [00:57.84] | cos 2 sin |
| [00:59.92] | tan 2 cot |
| [01:01.77] | tan 2 cot |
| [01:08.60] | That is to say the odds will change, evens are conserved |
| [01:13.47] | The notations that they get depend on where they are |
| [01:17.08] | But no matter where you are |
| [01:19.16] | I' ve gotta say that |
| [01:21.49] | If you were sine curve, I' d be your cosine curve |
| [01:25.73] | I' ll be your derivative, you' ll be my negtive one |
| [01:29.76] | As you change you amplitude, I change my phase |
| [01:34.17] | We can oscillate freely in the external space |
| [01:38.44] | As we change our period and costant at hand |
| [01:42.61] | We travel from the origin to infinity |
| [01:46.85] | It' s you sine, and you cosine |
| [01:51.27] | Who make charming music around the world |
| [01:55.45] | It' s you tangent, cotangent |
| [01:59.74] | Who proclaim the true meaning of centrosymmetry |
| [02:03.44] | B BOX |
| [02:46.93] | You wanna measure width of a river, height of a tower |
| [02:49.27] | You scratch your head which cost you more than an hour |
| [02:51.40] | You don' t need to ask any " gods" or" master" for help |
| [02:53.49] | This group of formulas are gonna help you solve |
| [02:55.82] | sin sin cos cos sin |
| [02:58.94] | cos cos cos sin sin |
| [03:02.22] | tan tan tan 1tan tan |
| [03:06.25] | sin sin cos cos sin |
| [03:09.59] | cos cos cos sin sin |
| [03:12.93] | tan tan tan 1 tan tan |
| [03:17.99] | As you come across a right triangle you fell easy to sovle |
| [03:20.23] | But an obtuse triange' s gonna make you feel confused |
| [03:22.26] | Don' t worry about what you do |
| [03:23.64] | There are always means to solve |
| [03:24.80] | As long as you master the sine cosine law |
| [03:30.04] | At this momnet I' ve got nothing to say |
| [03:33.80] | As trigfunctions rain down upon me |
| [03:38.45] | At this momnet I' ve got nothing to say |
| [03:42.52] | Let' s sing a song about trigfunctios |
| [03:47.13] | Long live the trigonometric functions |
| [03:55.85] |
| [00:10.56] | 当你初学数学中的1234 |
| [00:11.80] | 当你初学数学中的1234 |
| [00:12.88] | 初学方程中的XYZT |
| [00:13.97] | 初学方程中的XYZT |
| [00:14.94] | 它将帮助你进行逻辑思考 |
| [00:16.11] | 它将帮助你进行逻辑思考 |
| [00:16.96] | 当你唱起正弦，余弦，余弦，正切 |
| [00:18.27] | 当你唱起正弦，余弦，余弦，正切 |
| [00:19.28] | 正弦，余弦，正切，余切 |
| [00:20.25] | 正弦，余弦，正切，余切 |
| [00:21.40] | 正弦，余弦，正割，余割 |
| [00:22.34] | 正弦，余弦，正割，余割 |
| [00:23.57] | 让我们唱起三角函数的歌谣吧 |
| [00:24.54] | 让我们唱起三角函数的歌谣吧 |
| [00:25.25] | 诱导公式 |
| [00:25.82] | sin（2π+α）=sinα |
| [00:27.94] | cos（2π+α）=cosα |
| [00:29.89] | tan（2π+α）=tanα |
| [00:31.83] | 这是诱导公式归类1，下面是诱导公式归类2 |
| [00:34.23] | sin（π+α）= —sinα |
| [00:36.35] | cos（π+α）=—cosα |
| [00:38.63] | tan（π+α）= tanα |
| [00:40.69] | sin（π－α）= sinα |
| [00:42.53] | cos（π－α）=－cosα |
| [00:44.99] | tan（π－α）=－tanα |
| [00:47.11] | 这些均为“函数名不变” |
| [00:48.56] | 这些均为“函数名不变” |
| [00:49.29] | 当π成为π/2是变化会很大 |
| [00:50.32] | 当π成为π/2是变化会很大 |
| [00:51.36] | sin（π/2+α）=cosα |
| [00:53.48] | sin（π/2－α）=cosα |
| [00:55.45] | cos（π/2+α）=－sinα |
| [00:57.84] | cos（π/2－α）=sinα |
| [00:59.92] | tan（π/2+α）=－cotα |
| [01:01.77] | tan（π/2－α）=cotα |
| [01:08.60] | 这就是说 ：奇变偶不变 |
| [01:13.47] | 符号看象限 |
| [01:14.92] | 这就是说 “奇变偶不变，符号看象限 ” |
| [01:17.08] | 但不论你在哪 |
| [01:18.37] | 但不论你在哪 |
| [01:19.16] | 我将会说 |
| [01:20.24] | 我将会说 |
| [01:21.49] | 你若为正弦曲线，我愿做余弦曲线 |
| [01:22.65] | 你若为正弦曲线，我愿做余弦曲线 |
| [01:25.73] | 我将为你的导数，你将为我负导数 |
| [01:26.94] | 我将为你的导数，你将为我负导数 |
| [01:29.76] | 当你改变振幅，我改变相位 |
| [01:32.08] | 当你改变振幅，我改变相位 |
| [01:34.17] | 我们可在外界空间自由震荡 |
| [01:36.35] | 我们可在外界空间自由震荡 |
| [01:38.44] | 当我们改变周期和手边常数 |
| [01:40.79] | 当我们改变周期和手边常数 |
| [01:42.61] | 我们从原点驶向无尽 |
| [01:44.98] | 我们从原点驶向无尽 |
| [01:46.85] | 是你，正弦，余弦 |
| [01:48.80] | 是你，正弦，余弦 |
| [01:51.27] | 创造了世间动人的音乐 |
| [01:54.37] | 创造了世间动人的音乐 |
| [01:55.45] | 是你，正切，余切 |
| [01:57.46] | 是你，正切，余切 |
| [01:59.74] | 揭示了中心对称的真谛 |
| [02:01.02] | 揭示了中心对称的真谛 |
| [02:03.44] | B BOX表演已开始 |
| [02:46.93] | 你想测量河宽及塔高 |
| [02:48.26] | 你想测量河宽及塔高 |
| [02:49.27] | 你抓耳挠腮一个多小时也想不出 |
| [02:50.36] | 你抓耳挠腮一个多小时也想不出 |
| [02:51.40] | 你无需向dalao们请教 |
| [02:52.55] | 你无需向dalao们请教 |
| [02:53.49] | 这一组公式将帮你解决 |
| [02:54.52] | 这一组公式将帮你解决 |
| [02:55.50] | 恒等变换 |
| [02:55.82] | sin(α+β)=sinα•cosβ+cosα•sinβ |
| [02:58.94] | cos(α+β)=cosα•cosβ-sinα•sinβ |
| [03:02.22] | tan(α+β)=(tanα+tanβ)/(1-tanα•tanβ) |
| [03:06.25] | sin(α-β)=sinα•cosβ-cosα•sinβ |
| [03:09.59] | cos(α-β)=cosα•cosβ+sinα•sinβ |
| [03:12.93] | tan(α-β)=(tanα-tanβ)/(1+tanα•tanβ） |
| [03:17.99] | 当你遇到直角三角形很容易解 |
| [03:19.65] | 当你遇到直角三角形很容易解 |
| [03:20.23] | 但钝角三角形使你感到困惑 |
| [03:21.20] | 但钝角三角形使你感到困惑 |
| [03:22.26] | 无须担心 |
| [03:23.12] | 无须担心 |
| [03:23.64] | 总有解决方法 |
| [03:24.27] | 总有解决方法 |
| [03:24.80] | 只要你掌握了正余弦定理 |
| [03:25.68] | 只要你掌握了正余弦定理 |
| [03:30.04] | 此刻我无以言表 |
| [03:32.04] | 此刻我无以言表 |
| [03:33.80] | 当时三角函数犹雨点般落向我 |
| [03:36.11] | 当时三角函数犹雨点般落向我 |
| [03:38.45] | 此刻我无以言表 |
| [03:40.63] | 此刻我无以言表 |
| [03:42.52] | 让我们唱起三角函数歌谣吧 |
| [03:44.42] | 让我们唱起三角函数歌谣吧 |
| [03:47.13] | 三角函数万岁 |
| [03:50.32] | 三角函数万岁 |
YouTube搜索结果 (转至YouTube)