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好听的音乐：trigonometric functions (Single Version)-天儿

三角函数之歌 - 天儿
TME享有本翻译作品的著作权
When you first study math about 1234
当你初学数学时 要先从最简单的数字开始
First study equation about xyzt
然后深入了解方程式 搞懂xyzt的概念
It will help you to think in a logical
这将帮助你提升逻辑思维
Way
能力
When you sing sine cosine cosine tangent
当你学会了正弦 余弦 正切和余切
Sine cosine tangent cotangent
正弦 余弦 正切 余切
Sine cosine secant cosecant
正弦 余弦 正割 余割
Let\'s sing a song about trig functions
让我们来用一首歌记住这些三角函数吧
sin（2π+α）=sinα

cos（2π+α）=cosα

tan（2π+α）=tanα

Which is induction formula1
这些就是三角函数的
And induction formula 2
周期性规律
sin（π+α）= —sinα

cos（π+α）=—cosα

tan（π+α）= tanα

sin（π－α）= sinα

cos（π－α）=－cosα

tan（π－α）=－tanα

These are all those name donot change
这些都是函数名不变
As pi goes to half pi the difference shall be huge
当π成为π/2时 结果就会有显著的变化
sin（π/2+α）=cosα

sin（π/2－α）=cosα

cos（π/2+α）=－sinα

cos（π/2－α）=sinα

tan（π/2+α）=－cotα

tan（π/2－α）=cotα

That is to say the odds will change evens are conserved
也就是说 奇变偶不变
The notations that they get depend on where they are
符号看象限
But no matter where you are
但不管你在哪
I‘ve gotta say that
我想对你说
If you were sine curve I\'d be your cosine curve
若你愿做我的正弦曲线 那我就做你的余弦曲线
I\'ll be your derivative you\'ll be my negtive one
我是你的导数 你就是我的负导数
As you change you amplitude I change my phase
当你改变振幅时 我也会改变相位
We can oscillate freely in the external space
我们可以在外界空间自由振荡
As we change our period and costant at hand
当我们改变周期和常数时
We travel from the origin to infinity
我们可以从原点走到无穷远
It\'s you sine and you cosine
你就是那正弦 余弦
Who make charming music around the world
是你创造了动人的音乐
It\'s you tangent cotangent
你就是那正切 余切
Who proclaim the true meaning of centrosymmetry
你揭晓了中心对称的真谛
You wanna measure width of a river height of a tower
你想测量河流的宽度或塔楼的高度时
You scratch your head which cost you more than an hour
你抓耳挠腮 你冥思苦想了一个多小时
You don\'t need to ask any \"gods\" or\" master\" for help
但你无需向大神们请教
This group of formulas are gonna help you solve
因为下面这组公式就能帮你解决
sin(α+β)=sinα•cosβ+cosα•sinβ

cos(α+β)=cosα•cosβ-sinα•sinβ

tan(α+β)=(tanα+tanβ)/(1-tanα•tanβ)

sin(α-β)=sinα•cosβ-cosα•sinβ

cos(α-β)=cosα•cosβ+sinα•sinβ

tan(α-β)=(tanα-tanβ)/(1+tanα•tanβ)

As you come across a right triangle you fell easy to sovle
当你遇到直角三角形时 你很容易就能解决
But an obtuse triange\'s gonna make you feel confused
但钝角三角形可能会让你感到困惑
Don\'t worry about what you do
你也无需焦虑
There are always means to solve
只要你掌握了正弦余弦定律
As long as you master the sine cosine law
总会有方法解决的
At this momnet i\'ve got nothing to say
此刻 我已无需多说
As trig functions rain down upon me
因为三角函数的内容真的太多了
At this momnet i\'ve got nothing to say
此刻 我已无需多说
Let\'s sing a song about trig functios
让我们来用一首歌记住这些三角函数吧
Long live the trigonometric functions
三角函数万岁

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