trigonometricfunctions(SingleVersion) 天儿 歌词

trigonometric functions - 天儿

TME享有本翻译作品的著作权

词：天儿

曲：天儿

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

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 solve

当你遇到直角三角形时 你很容易就能解决

But an obtuse triangle 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 moment 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 moment I've got nothing to say

此刻 我已无需多说

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

Long live the trigonometric functions

三角函数万岁