當你唱著 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
讓我們唱起這首三角函數(shù)之歌
sin（2π+α）=sinα
cos（2π+α）=cosα
tan（2π+α）=tanα
which is induction formula1 and induction formula 2
這是第一類誘導公式 接下來是第二類誘導公式
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
這些都是函數(shù)名不變
As pi goes to half pi the difference shall be huge
當π值縮小一半 結(jié)果會大不相同
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
這就是說 奇變偶不變
The notations that they get depend on where they are
符號看象限
But no matter where you are
可是無論你在哪里
I’ve gotta say that
我都會說
If you were sine curve I’d be your cosine curve
如果你是正弦函數(shù) 我愿做你的余弦函數(shù)
I’ll be your derivative you’ll be my negtive one
我會成為你的導數(shù) 而你是我的負導數(shù)
As you change you amplitude I change my phase
當你改變振幅時 我會改變相位
We can oscillate freely in the external space
我們可以在外空間自由地波動
As we change our period and costant at hand
當我們改變周期和身旁的常數(shù)時
We travel from the origin to infinity
我們可以從原點一直到無窮盡
It’s you sine and you cosine
正是你 正弦和余弦
Who make charming music around the world
創(chuàng)造了這世上最動聽的音樂
It’s you tangent cotangent
正是你 正切和余切
Who proclaim the true meaning of centrosymmetry
揭示了中心對稱的真正含義
You wanna measure width of a river height of a tower
你想要測量河流的寬度以及塔的高度
You scratch your head which cost you more than an hour
你抓耳撓腮 冥思苦想了一小時也無濟于事
You don’t need to ask any “gods” or” master” for help
你無需向上帝或是偉人請求幫助
This group of formulas are gonna help you solve
以下這組公式讓你的難題迎刃而解
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 sovle
當你遇到直角三角形時 你覺得很容易解決
But an obtuse triange’s gonna make you feel confused
可是鈍角三角形讓你感到困惑
Don’t worry about what you do
不必擔心 不必手足無措
There are always means to solve
總會找到解決辦法
As long as you master the sine cosine law
只要你掌握了正余弦定理
At this momnet I’ve got nothing to say
此刻我一言不發(fā)
As trig-functions rain down upon me
當三角函數(shù)如雨點一般落在我身上
At this momnet I’ve got nothing to say
此刻我一言不發(fā)
Let’s sing a song about trig-functios
讓我們唱起這首三角函數(shù)之歌
Long live the trigonometric functions
三角函數(shù)萬歲
