When you first study math about 1234
你初次学习数学是从1 2 3 4开始的
First study equation about xyzt
你初次学习方程是从包含x y z t的方程式开始的
It will help you to think in a logical way
这有助你进行逻辑思考
When you sing sine cosine cosine tangent
当你唱着 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
让我们唱起这首三角函数之歌
sin(2π+α)=sinα
cos(2π+α)=cosα
tan(2π+α)=tanα
Which is induction formula1 and induction formula 2
这是第一类诱导公式 接下来是第二类诱导公式
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 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值缩小一半 结果会大不相同
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
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
可是无论你在哪里
I've gotta say that
我都会说
If you were sine curve I'd be your cosine curve
如果你是正弦函数 我愿做你的余弦函数
I'll be your derivative you'll be my negative one
我会成为你的导数 而你是我的负导数
As you change your amplitude I change my phase
当你改变振幅时 我会改变相位
We can oscillate freely in the external space
我们可以在外空间自由地波动
As we change our period and constant at hand
当我们改变周期和身旁的常数时
We travel from the origin to infinity
我们可以从原点一直到无穷尽
It's you sine and you cosine
正是你 正弦和余弦
Who make charming music around the world
创造了这世上最动听的音乐
It's you tangent cotangent
正是你 正切和余切
Who proclaim the true meaning of centrosymmetry
揭示了中心对称的真正含义
You wanna measure width of a river height of a tower
你想要测量河流的宽度以及塔的高度
You scratch your head which cost you more than an hour
你抓耳挠腮 冥思苦想了一小时也无济于事
You don't need to ask any "gods" or" master" for help
你无需向上帝或是伟人请求帮助
This group of formulas are gonna help you solve
以下这组公式让你的难题迎刃而解
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 solve
当你遇到直角三角形时 你觉得很容易解决
But an obtuse triangle's gonna make you feel confused
可是钝角三角形让你感到困惑
Don't worry about what you do
不必担心 不必手足无措
There are always means to solve
总会找到解决办法
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
此刻我一言不发
As trig-functions rain down upon me
当三角函数如雨点一般落在我身上
At this moment I've got nothing to say
此刻我一言不发
Let's sing a song about trig-functions
让我们唱起这首三角函数之歌
Long live the trigonometric functions
......
当时我听到这首歌时,整个人都麻了
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