Song of Trigonometric Functions "妙趣横生，旋律婉转，数学与音乐的完美交融 ——《三角函数之歌》引领你探索数学的音符奇迹！"

简介：

这是一首充满数学韵味的歌曲，旨在以轻快的旋律和幽默的歌词呈现关于三角函数的基本概念。歌曲以初学数学的1234为背景，探讨了关于xyzt的方程，引导听众以逻辑方式思考数学问题。

从正弦、余弦、正切到和差角公式，歌曲生动地描绘了三角函数的性质和公式。通过引入数学中的诸多概念，如π的变化和奇偶性的保持，歌曲旨在用欢快的音乐为学习三角函数提供趣味和动力。

同时，歌曲通过有趣的比喻，将三角函数彼此之间的关系与人际关系相类比，为抽象的数学概念增添了亲和力。正弦曲线与余弦曲线之间的关系被幽默地比作人际关系，给听众带来一种轻松而愉悦的学习体验。

在歌曲的高潮部分，强调了三角函数在解决实际问题中的应用，以及正弦余弦定律的重要性。整首歌旨在激发对数学的兴趣，让学习者更加享受数学之美，同时向三角函数致以崇敬之情。

《三角函数之歌》（伴奏）
   • Song of Trigonometric Functions (Musi...  

Synopsis:

This is a maths-inspired song designed to present basic concepts about trigonometry with a light-hearted melody and humorous lyrics. Set against the backdrop of 1234, a beginner's maths, the song explores equations about xyzt, guiding the listener to think about maths in a logical way.

From sine, cosine, and tangent to the sum and difference angle formulas, the song vividly depicts the properties and formulas of trigonometric functions. By introducing many concepts in mathematics, such as the variation of π and the preservation of parity, the song aims to provide fun and motivation for learning trigonometry with upbeat music.

At the same time, the song adds relatability to abstract mathematical concepts by using interesting analogies to how trigonometric functions relate to each other and to human relationships. The relationship between the sine curve and the cosine curve is humourously compared to human relationships, giving the listener a relaxing and enjoyable learning experience.

In the climax of the song, the application of trigonometric functions in solving practical problems and the importance of the law of sines and cosines are emphasised. The whole song aims to stimulate interest in mathematics and make learners enjoy the beauty of mathematics more, while paying tribute to trigonometric functions.

Song of Trigonometric Functions (Accompaniment)
   • Song of Trigonometric Functions (Musi...  

引用 Quote：   • All 6 Trig Functions on the Unit Circle   0:35 - 3:10

作者/原唱：映射者天儿
翻唱：讲不清

歌词 Lyrics：

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

cos（2π+α）=cosα

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

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

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

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

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