當(dāng)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(lèi)誘導(dǎo)公式 接下來(lái)是第二類(lèi)誘導(dǎo)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(dāng)π值縮小一半 結(jié)果會(huì)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(shuō) 奇變偶不變
The notations that they get depend on where they are
符號(hào)看象限
But no matter where you are
可是無(wú)論你在哪里
I’ve gotta say that
我都會(huì)說(shuō)
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(huì)成為你的導(dǎo)數(shù) 而你是我的負(fù)導(dǎo)數(shù)
As you change you amplitude I change my phase
當(dāng)你改變振幅時(shí) 我會(huì)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(dòng)
As we change our period and costant at hand
當(dāng)我們改變周期和身旁的常數(shù)時(shí)
We travel from the origin to infinity
我們可以從原點(diǎn)一直到無(wú)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(dòng)聽(tīng)的音樂(lè)
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(duì)稱(chēng)的真正含義
You wanna measure width of a river height of a tower
你想要測(cè)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(shí)也無(wú)濟(jì)于事
You don’t need to ask any “gods” or” master” for help
你無(wú)需向上帝或是偉人請(qǐng)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(dāng)你遇到直角三角形時(shí) 你覺(jué)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?fù)?dān)心 不必手足無(wú)措
There are always means to solve
總會(huì)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(dāng)三角函數(shù)如雨點(diǎn)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(wàn)歲
