trigonometric functions-映射者天儿

[00:00.000] 作词 : 映射者 [00:01.000] 作曲 : 映射者 [00:10.56]when you first study math about 1234
当你初学数学中的1234 [00:12.88]first study equation about xyzt
初学方程中的XYZT [00:14.94]It will help you to think in a logical way
它将帮助你进行逻辑思考 [00:16.96]When you sing sine, cosine, cosine, tangent
当你唱起正弦，余弦，余弦，正切 [00:19.28]Sine, cosine, tangent, cotangent
正弦，余弦，正切，余切 [00:21.40]Sine, cosine, ..., secant, cosecant
正弦，余弦，正割，余割 [00:23.57]Let's sing a song about trig-functions
让我们唱起三角函数的歌谣吧 [00:25.82]sin（2π+α）=sinα
sin（2π+α）=sinα [00:27.94]cos（2π+α）=cosα
cos（2π+α）=cosα [00:29.89]tan（2π+α）=tanα
tan（2π+α）=tanα [00:31.83]which is induction formula1, and induction formula 2
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
sin（π+α）= —sinα [00:36.35]cos（π+α）=—cosα
cos（π+α）=—cosα [00:38.63]tan（π+α）= tanα
tan（π+α）= tanα [00:40.69]sin（π－α）= sinα
sin（π－α）= sinα [00:42.53]cos（π－α）=－cosα
cos（π－α）=－cosα [00:44.99]tan（π－α）=－tanα
tan（π－α）=－tanα [00:47.11]These are all those "name donot change"
这些均为“函数名不变” [00:49.29]As pi goes to half pi the difference shall be huge
当π成为π/2是变化会很大 [00:51.36]sin（π/2+α）=cosα
sin（π/2+α）=cosα [00:53.48]sin（π/2－α）=cosα
sin（π/2－α）=cosα [00:55.45]cos（π/2+α）=－sinα
cos（π/2+α）=－sinα [00:57.84]cos（π/2－α）=sinα
cos（π/2－α）=sinα [00:59.92]tan（π/2+α）=－cotα
tan（π/2+α）=－cotα [01:01.77]tan（π/2－α）=cotα
tan（π/2－α）=cotα [01:08.60]That is to say the odds will change, evens are conserved
这就是说 ：奇变偶不变 [01:13.47]The notations that they get depend on where they are
符号看象限 [01:17.08]But no matter where you are
但不论你在哪 [01:19.16]I've gotta say that
我将会说 [01:21.49]If you were my sine curve, I'd be your cosine curve
你若为正弦曲线，我愿做余弦曲线 [01:25.73]I'll be your derivative, you'll be my negative one
我将为你的导数，你将为我负导数 [01:29.76]As you change you amplitude, I change my phase
当你改变振幅，我改变相位 [01:34.17]We can oscillate freely in the external space
我们可在外界空间自由震荡 [01:38.44]As we change our period and costant at hand
当我们改变周期和手边常数 [01:42.61]We travel from the origin to infinity
我们从原点驶向无尽 [01:46.85]It's you sine, and you cosine
是你，正弦，余弦 [01:51.27]Who make charming music around the world
创造了世间动人的音乐 [01:55.45]It's you tangent, cotangent
是你，正切，余切 [01:59.74]Who proclaim the true meaning of centrosymmetry
揭示了中心对称的真谛 [02:03.44]B BOX
B BOX表演已开始 [02:46.93]You wanna measure width of a river, height of a tower
你想测量河宽及塔高 [02:49.27]You scratch your head which cost you more than an hour
你抓耳挠腮一个多小时也想不出 [02:51.40]You don't need to ask any "gods" or" master" for help
你无需向大佬们请教 [02:53.49]This group of formulas are gonna help you solve
这一组公式将帮你解决 [02:55.82]sin(α+β)=sinα•cosβ+cosα•sinβ
sin(α+β)=sinα•cosβ+cosα•sinβ [02:58.94]cos(α+β)=cosα•cosβ-sinα•sinβ
cos(α+β)=cosα•cosβ-sinα•sinβ [03:02.22]tan(α+β)=(tanα+tanβ)/(1-tanα•tanβ)
tan(α+β)=(tanα+tanβ)/(1-tanα•tanβ) [03:06.25]sin(α-β)=sinα•cosβ-cosα•sinβ
sin(α-β)=sinα•cosβ-cosα•sinβ [03:09.59]cos(α-β)=cosα•cosβ+sinα•sinβ
cos(α-β)=cosα•cosβ+sinα•sinβ [03:12.93]tan(α-β)=(tanα-tanβ)/(1+tanα•tanβ)
tan(α-β)=(tanα-tanβ)/(1+tanα•tanβ） [03:17.99]As you come across a right triangle you fell easy to solve
当你遇到直角三角形很容易解 [03:20.23]But an obtuse triange gonna make you feel confused
但钝角三角形使你感到困惑 [03:22.26]Don't worry about what you do
无须担心 [03:23.64]There are always means to solve
总有解决方法 [03:24.80]As long as you master the sine cosine law
只要你掌握了正余弦定理 [03:30.04]At this moment I've got nothing to say
此刻我无以言表 [03:33.80]As trig-functions rain down upon me
当时三角函数犹雨点般落向我 [03:38.45]At this moment I've got nothing to say
此刻我无以言表 [03:42.52]Let's sing a song about trig-functions
让我们唱起三角函数歌谣吧 [03:47.13]Long live the trigonometric functions
三角函数万岁 [03:55.85]