《英语之三角函数之歌》 我分不清究竟是阿英歹毒还是阿数更歹毒。#我很少用歹毒来形容一首歌# 《英语之三角函数之歌》我分不清究竟是阿英歹毒还是阿数更歹毒泪。
英语之三角函数之歌(中英文互译版)
when you first study math about 1234
当你初学数学中的1234
first study equation about xyzt
初学方程中的XYZT
It will help you to think in a logical way
它将帮助你进行逻辑思考
When you sing sine, cosine, cosine, tangent
当你唱起正弦，余弦，余弦，正切
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
让我们唱起三角函数的歌谣吧
sin（2π+α）=sinα
sin（2π+α）=sinα
cos（2π+α）=cosα
cos（2π+α）=cosα
tan（2π+α）=tanα
tan（2π+α）=tanα
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
sin（π+α）= —sinα
sin（π+α）= —sinα
cos（π+α）=—cosα
cos（π+α）=—cosα
tan（π+α）= tanα
tan（π+α）= tanα
sin（π－α）= sinα
sin（π－α）= sinα
cos（π－α）=－cosα
cos（π－α）=－cosα
tan（π－α）=－tanα
tan（π－α）=－tanα
These are all those "name donot change"
这些均为“函数名不变”
As pi goes to half pi the difference shall be huge
当π成为π/2是变化会很大
sin（π/2+α）=cosα
sin（π/2+α）=cosα
sin（π/2－α）=cosα
sin（π/2－α）=cosα
cos（π/2+α）=－sinα
cos（π/2+α）=－sinα
cos（π/2－α）=sinα
cos（π/2－α）=sinα
tan（π/2+α）=－cotα
tan（π/2+α）=－cotα
tan（π/2－α）=cotα
tan（π/2－α）=cotα
That is to say the odds will change, evens are conserved
这就是说 ：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
但不论你在哪
I've gotta say that
我将会说
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
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
As you change you amplitude, I change my phase
当你改变振幅，我改变相位
We can oscillate freely in the external space
我们可在外界空间自由震荡
As we change our period and costant at hand
当我们改变周期和手边常数
We travel from the origin to infinity
我们从原点驶向无尽
It's you sine, and you cosine
是你，正弦，余弦
Who make charming music around the world
创造了世间动人的音乐
It's you tangent, cotangent
是你，正切，余切
Who proclaim the true meaning of centrosymmetry
揭示了中心对称的真谛
No B BOX
没有B BOX
You wanna measure width of a river, height of a tower
你想测量河宽及塔高
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
You don't need to ask any "gods" or" master" for help
你无需向大佬们请教
This group of formulas are gonna help you solve
这一组公式将帮你解决
sin(α+β)=sinα•cosβ+cosα•sinβ
sin(α+β)=sinα•cosβ+cosα•sinβ
cos(α+β)=cosα•cosβ-sinα•sinβ
cos(α+β)=cosα•cosβ-sinα•sinβ
tan(α+β)=(tanα+tanβ)/(1-tanα•tanβ)
tan(α+β)=(tanα+tanβ)/(1-tanα•tanβ)
sin(α-β)=sinα•cosβ-cosα•sinβ
sin(α-β)=sinα•cosβ-cosα•sinβ
cos(α-β)=cosα•cosβ+sinα•sinβ
cos(α-β)=cosα•cosβ+sinα•sinβ
tan(α-β)=(tanα-tanβ)/(1+tanα•tanβ)
tan(α-β)=(tanα-tanβ)/(1+tanα•tanβ）
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
But an obtuse triange gonna make you feel confused
但钝角三角形使你感到困惑
Don't worry about what you do
无须担心
There are always means to solve
总有解决方法
As long as you master the sine cosine law
只要你掌握了正余弦定理
At this moment I've got nothing to say
此刻我无以言表
As trig-functions rain down upon me
当时三角函数犹雨点般落向我
At this moment I've got nothing to say
此刻我无以言表
Let's sing a song about trig-functions
让我们唱起三角函数歌谣吧
Long live the trigonometric functions
三角函数万岁
