三角函数之歌中文版歌词，歌词翻译来了！

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