TrigonometricFunctions（三角函数之歌）

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 way

这将帮助你提升逻辑思维能力

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 and induction formula 2

这些就是三角函数的周期性规律

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 do not -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

cos(π/2+α)=-sinα

tan(π/2+α)=-cotα

sin(π/2-α)=cosα

cos(π/2-α)=sinα

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 my 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 negative 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