trigonometric functions - 天儿

[00:00.0]trigonometric functions - 天儿
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[00:02.26]词：天儿
[00:03.09]
[00:03.09]曲：天儿
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[00:10.6]When you first study math about 1234
[00:12.91]你初次学习数学是从1 2 3 4开始的
[00:12.91]First study equation about xyzt
[00:14.83]你初次学习方程是从包含x y z t的方程式开始的
[00:14.83]It will help you to think in a logical way
[00:16.9]这有助你进行逻辑思考
[00:16.9]When you sing sine cosine cosine tangent
[00:19.33]当你唱着 正弦 余弦 余弦 正切
[00:19.33]Sine cosine tangent cotangent
[00:21.48]正弦 余弦 正切 余切
[00:21.48]Sine cosine secant cosecant
[00:23.61]正弦 余弦 正割 余割
[00:23.61]Let's sing a song about trig-functions
[00:25.72]让我们唱起这首三角函数之歌
[00:25.72]sin(2π+α)=sinα
[00:27.87]
[00:27.87]cos(2π+α)=cosα
[00:30.02]
[00:30.02]tan(2π+α)=tanα
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[00:31.92]Which is induction formula1 and induction formula 2
[00:34.3]这是第一类诱导公式 接下来是第二类诱导公式
[00:34.3]sin(π+α)= -sinα
[00:36.46]
[00:36.46]cos(π+α)=-cosα
[00:38.66]
[00:38.66]tan(π+α)= tanα
[00:40.69]
[00:40.69]sin(π-α)= sinα
[00:42.85]
[00:42.85]cos(π-α)=-cosα
[00:45.02]
[00:45.02]tan(π-α)=-tanα
[00:47.22]
[00:47.22]These are all those "name do not -change"
[00:49.21]这些都是函数名不变
[00:49.21]As pi goes to half pi the difference shall be huge
[00:51.69]当π值缩小一半 结果会大不相同
[00:51.69]sin(π/2+α)=cosα
[00:53.71]
[00:53.71]cos(π/2+α)=-sinα
[00:55.76]
[00:55.76]tan(π/2+α)=-cotα
[00:58.11]
[00:58.11]sin(π/2-α)=cosα
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[01:00.0]cos(π/2-α)=sinα
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[01:02.14]tan(π/2-α)=cotα
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[01:08.8]That is to say the odds will change evens are conserved
[01:12.7]这就是说 奇变偶不变
[01:12.7]The notations that they get depend on where they are
[01:16.97]符号看象限
[01:16.97]But no matter where you are
[01:19.36]可是无论你在哪里
[01:19.36]I've gotta say that
[01:21.47]我都会说
[01:21.47]If you were my sine curve I'd be your cosine curve
[01:25.78]如果你是正弦函数 我愿做你的余弦函数
[01:25.78]I'll be your derivative you'll be my negative one
[01:30.09]我会成为你的导数 而你是我的负导数
[01:30.09]As you change you amplitude I change my phase
[01:33.979996]当你改变振幅时 我会改变相位
[01:33.979996]We can oscillate freely in the external space
[01:38.54]我们可以在外空间自由地波动
[01:38.54]As we change our period and costant at hand
[01:42.61]当我们改变周期和身旁的常数时
[01:42.61]We travel from the origin to infinity
[01:47.16]我们可以从原点一直到无穷尽
[01:47.16]It's you sine and you cosine
[01:51.46]正是你 正弦和余弦
[01:51.46]Who make charming music around the world
[01:55.55]创造了这世上最动听的音乐
[01:55.55]It's you tangent cotangent
[01:59.759995]正是你 正切和余切
[01:59.759995]Who proclaim the true meaning of centrosymmetry
[02:47.09]揭示了中心对称的真正含义
[02:47.09]You wanna measure width of a river height of a tower
[02:49.42]你想要测量河流的宽度以及塔的高度
[02:49.42]You scratch your head which cost you more than an hour
[02:51.45]你抓耳挠腮 冥思苦想了一小时也无济于事
[02:51.45]You don't need to ask any "gods" or" master" for help
[02:53.62]你无需向上帝或是伟人请求帮助
[02:53.62]This group of formulas are gonna help you solve
[02:55.75]以下这组公式让你的难题迎刃而解
[02:55.75]sin(α+β)=sinα•cosβ+cosα•sinβ
[02:59.0]
[02:59.0]cos(α+β)=cosα•cosβ-sinα•sinβ
[03:02.32]
[03:02.32]tan(α+β)=(tanα+tanβ)/(1-tanα•tanβ)
[03:06.45]
[03:06.45]sin(α-β)=sinα•cosβ-cosα•sinβ
[03:09.8]
[03:09.8]cos(α-β)=cosα•cosβ+sinα•sinβ
[03:12.93]
[03:12.93]tan(α-β)=(tanα-tanβ)/(1+tanα•tanβ)
[03:18.1]
[03:18.1]As you come across a right triangle you fell easy to solve
[03:20.41]当你遇到直角三角形时 你觉得很容易解决
[03:20.41]But an obtuse triangle gonna make you feel confused
[03:22.52]可是钝角三角形让你感到困惑
[03:22.52]Don't worry about what you do
[03:23.65]不必担心 不必手足无措
[03:23.65]There are always means to solve
[03:24.7]总会找到解决办法
[03:24.7]As long as you master the sine cosine law
[03:30.25]只要你掌握了正余弦定理
[03:30.25]At this moment I've got nothing to say
[03:34.14]此刻我一言不发
[03:34.14]As trig-functions rain down upon me
[03:38.69]当三角函数如雨点一般落在我身上
[03:38.69]At this moment I've got nothing to say
[03:42.65]此刻我一言不发
[03:42.65]Let's sing a song about trig-functions
[03:47.22]让我们唱起这首三角函数之歌
[03:47.22]Long live the trigonometric functions
[03:52.022]三角函数万岁