trigonometric functions

when you first study math about 1234
當你初學數學中的1234
first study equation about xyzt
初學方程中的XYZT
It will help you to think in a logical way
它將幫助你進行邏輯思考
When you sing sine,cosine,cosine,tangent
當你唱起正弦，餘弦，餘弦，正切
Sine,cosine,tangent,cotangent
正弦，餘弦，正切，餘切
Sine,cosine,..,secant,cosecant
正弦，餘弦，正割，餘割
Lets sing a song about trig-functions
讓我們唱起三角函數的歌謠吧
sin（2π+α）=sinα
sin（2π+α）=sinα
cos（2π+α）=cosα
cos（2π+α）=cosα
tan （2π+α）=tanα
tan（2π+α）=tanα
which is induction formula1,and induction formula 2
這是誘導公式歸類1，下面是誘導公式歸類2
sin（π+α）= —sinα
sin（π+α）= —sinα
cos（π+α）=—cosα
cos（π+α）=—cosα
tan （π+α）= tanα
tan（π+α）= tanα
sin（π－α）= sinα
sin（π－α）= sinα
cos（π－α）= －cosα
cos（π－α）=－cosα
tan（π－α）=－tanα
tan（π－α）=－tanα
These are all those 'name donot -change '
這些均為“函數名不變”
As pi goes to half pi the difference shall be huge
當π成為π/2是變化會很大
sin（π/2+ α）=cosα
sin（π/2+α）=cosα
sin（π/2－α）=cosα
sin（π/2－α）=cosα
cos（π/ 2+α）=－sinα
cos（π/2+α）=－sinα
cos（π/2－α）=sinα
cos（π/2－α）=sinα
tan（π/2+α）=－cotα
tan（π/2+α）=－cotα
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
但不論你在哪
I've gotta say that
我將會說
If you were my sine curve,Id be your cosine curve
你若為正弦曲線，我願做餘弦曲線
Ill be your derivative,youll be my negtive one
我將為你的導數，你將為我負導數
As you change you amplitude,I change my phase
當你改變振幅，我改變相位
We can oscillate freely in the external space
我們可在外界空間自由震盪
As we change our period and costant at hand
當我們改變週期和手邊常數
We travel from the origin to infinity
我們從原點駛向無盡
Its you sine,and you cosine
是你，正弦，餘弦
Who make charming music around the world
創造了世間動人的音樂
Its you tangent,cotangent
是你，正切，餘切
Who proclaim the true meaning of centrosymmetry
揭示了中心對稱的真諦
B BOX
B BOX表演已開始
You wanna measure width of a river,height of a tower
你想測量河寬及塔高
You scratch your head which cost you more than an hour
你抓耳撓腮一個多小時也想不出
You dont need to ask any 'gods' or' master' for help
你無需向dalao們請教
This group of formulas are gonna help you solve
這一組公式將幫你解決
sin(α+β)=sinα•cosβ+cosα•sinβ
sin(α+β)=sinα•cosβ+cosα•sinβ
cos(α+β)=cosα•cosβ-sinα•sinβ
cos(α+β)=cosα•cosβ-sinα•sinβ
tan(α+β)=(tanα+tanβ)/(1-tanα•tanβ)
tan(α+β)=(tanα +tanβ)/(1-tanα•tanβ)
sin(α-β)=sinα•cosβ-cosα•sinβ
sin(α-β)=sinα•cosβ-cosα•sinβ
cos( α-β)=cosα•cosβ+sinα•sinβ
cos(α-β)=cosα•cosβ+sinα•sinβ
tan(α-β)=(tanα-tanβ)/(1+tanα• tanβ)
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很容易解
But an obtuse triange gonna make you feel confused
但鈍角三角形使你感到困惑
Dont worry about what you do
無須擔心
There are always means to solve
總有解決方法
As long as you master the sine cosine law
只要你掌握了正餘弦定理
At this momnet Ive got nothing to say
此刻我無以言表
As trig-functions rain down upon me
當時三角函數猶雨點般落向我
At this moment Ive got nothing to say
此刻我無以言表
Lets singa song about trig-functions
讓我們唱起三角函數歌謠吧
Long live the trigonometric functions
三角函數万歲