0trigonometric functions
天儿
[段落1 N1]
1when you first study math about 1234
~当你初学数学中的1234
2first study equation about xyzt
~初学方程中的XYZT
3It will help you to think in a logical way
~它将帮助你进行逻辑思考
4When you sing sine,cosine,cosine,tangent
~当你唱起正弦，余弦，余弦，正切
5Sine,cosine,tangent,cotangent
~正弦，余弦，正切，余切
6Sine,cosine,..,secant,cosecant
~正弦，余弦，正割，余割
7Let's sing a song about trig-functions
~让我们唱起三角函数的歌谣吧
[段落2 N2]
8sin(2π+α) = sinα
~sin(2π+α) = sinα
9cos(2π+α) = cosα
~cos(2π+α) = cosα
10tan(2π+α) = tanα
~tan(2π+α) = tanα
11which 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
12sin(π+α) = -sinα
~sin(π+α) = -sinα
13cos(π+α) = -cosα
~cos(π+α) = -cosα
14tan(π+α) = tanα
~tan(π+α) = tanα
15sin(π－α) = sinα
~sin(π－α) = sinα
16cos(π－α) = -cosα
~cos(π－α) = -cosα
17tan(π－α) = -tanα
~tan(π－α) = -tanα
18These are all those "name donot -change"
~这些均为“函数名不变”
[段落3 N3]
19As pi goes to half pi the difference shall be huge
~当π成为π/2是变化会很大
20sin(π/2+α) = cosα
~sin(π/2+α) = cosα
21cos(π/2-α) = sinα
~cos(π/2-α) = sinα
22sin(π/2-α) = cosα
~sin(π/2-α) = cosα
23cos(π/2+α) = -sinα
~cos(π/2+α) = -sinα
24tan(π/2+α) = -cotα
~tan(π/2+α) = -cotα
25tan(π/2-α) = cotα
~tan(π/2-α) = cotα
[段落4 N4]
26That is to say the odds will change, evens are conserved
~这就是说 ：奇变偶不变
27The notations that they get depend on where they are
~符号看象限
28But no matter where you are, I've gotta say that
~但不论你在哪，我将会说
29If 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
30I'll be your derivative,you'll be my negtive one
~我将为你的导数，你将为我负导数
31As you change you amplitude,I change my phase
~当你改变振幅，我改变相位
32We can oscillate freely in the external space
~我们可在外界空间自由震荡
33As we change our period and costant at hand
~当我们改变周期和手边常数
34We travel from the origin to infinity
~我们从原点驶向无尽
[段落5 N5]
35It's you sine,and you cosine
~是你，正弦，余弦
36Who make charming music around the world
~创造了世间动人的音乐
37It's you tangent,cotangent
~是你，正切，余切
38Who proclaim the true meaning of centrosymmetry
~揭示了中心对称的真谛
[间奏 --]
39- - - - - - -
[段落6 N6]
40You wanna measure width of a river,height of a tower
~你想测量河宽及塔高
41You scratch your head which cost you more than an hour
~你抓耳挠腮一个多小时也想不出
42You don't need to ask any "gods" or "master" for help
~你无需向dalao们请教
43This group of formulas are gonna help you solve
~这一组公式将帮你解决
44sin(α+β) = sinα•cosβ + cosα•sinβ
~sin(α+β) = sinα•cosβ + cosα•sinβ
45cos(α+β) = cosα•cosβ - sinα•sinβ
~cos(α+β) = cosα•cosβ - sinα•sinβ
46tan(α+β) = (tanα + tanβ) / (1 - tanα•tanβ)
~tan(α+β) = (tanα + tanβ) / (1 - tanα•tanβ)
47sin(α-β) = sinα•cosβ - cosα•sinβ
~sin(α-β) = sinα•cosβ - cosα•sinβ
48cos(α-β) = cosα•cosβ + sinα•sinβ
~cos(α-β) = cosα•cosβ + sinα•sinβ
49tan(α-β) = (tanα - tanβ) / (1 + tanα•tanβ)
~tan(α-β) = (tanα - tanβ)/(1 + tanα•tanβ)
50As you come across a right triangle you fell easy to sovle
~当你遇到直角三角形很容易解
51But an obtuse triange's gonna make you feel confused
~但钝角三角形使你感到困惑
52Don't worry about what you do
~无须担心
53There are always means to solve
~总有解决方法
54As long as you master the sine cosine law
~只要你掌握了正余弦定理
[段落7 N7]
55At this momnet I've got nothing to say
~此刻我无以言表
56As trig-functions rain down upon me
~当时三角函数犹雨点般落向我
57At this moment I've got nothing to say
~此刻我无以言表
58Let's sing a song about trig-functions
~让我们唱起三角函数歌谣吧
59Long live the trigonometric functions
~三角函数万岁
