trigonometric functions - 天儿

[00:00.000] 作词 : 天儿
[00:01.000] 作曲 : 天儿
[00:10.56]when you first study math about 1234
[00:12.88]first study equation about xyzt
[00:14.94]It will help you to think in a logical way
[00:16.96]When you sing sine, cosine, cosine, tangent
[00:19.28]Sine, cosine, tangent, cotangent
[00:21.40]Sine, cosine, ..., secant, cosecant
[00:23.57]Let's sing a song about trig-functions
[00:25.82]sin（2π+α）=sinα
[00:27.94]cos（2π+α）=cosα
[00:29.89]tan（2π+α）=tanα
[00:31.83]which is induction formula1, and induction formula 2
[00:34.23]sin（π+α）= —sinα
[00:36.35]cos（π+α）=—cosα
[00:38.63]tan（π+α）= tanα
[00:40.69]sin（π－α）= sinα
[00:42.53]cos（π－α）=－cosα
[00:44.99]tan（π－α）=－tanα
[00:47.11]These are all those \"name donot change\"
[00:49.29]As pi goes to half pi the difference shall be huge
[00:51.36]sin（π\/2+α）=cosα
[00:53.48]sin（π\/2－α）=cosα
[00:55.45]cos（π\/2+α）=－sinα
[00:57.84]cos（π\/2－α）=sinα
[00:59.92]tan（π\/2+α）=－cotα
[01:01.77]tan（π\/2－α）=cotα
[01:08.60]That is to say the odds will change, evens are conserved
[01:13.47]The notations that they get depend on where they are
[01:17.08]But no matter where you are
[01:19.16]I've gotta say that
[01:21.49]If you were my sine curve, I'd be your cosine curve
[01:25.73]I'll be your derivative, you'll be my negative one
[01:29.76]As you change you amplitude, I change my phase
[01:34.17]We can oscillate freely in the external space
[01:38.44]As we change our period and costant at hand
[01:42.61]We travel from the origin to infinity
[01:46.85]It's you sine, and you cosine
[01:51.27]Who make charming music around the world
[01:55.45]It's you tangent, cotangent
[01:59.74]Who proclaim the true meaning of centrosymmetry
[02:03.44]B BOX
[02:46.93]You wanna measure width of a river, height of a tower
[02:49.27]You scratch your head which cost you more than an hour
[02:51.40]You don't need to ask any \"gods\" or\" master\" for help
[02:53.49]This group of formulas are gonna help you solve
[02:55.82]sin(α+β)=sinα•cosβ+cosα•sinβ
[02:58.94]cos(α+β)=cosα•cosβ-sinα•sinβ
[03:02.22]tan(α+β)=(tanα+tanβ)\/(1-tanα•tanβ)
[03:06.25]sin(α-β)=sinα•cosβ-cosα•sinβ
[03:09.59]cos(α-β)=cosα•cosβ+sinα•sinβ
[03:12.93]tan(α-β)=(tanα-tanβ)\/(1+tanα•tanβ)
[03:17.99]As you come across a right triangle you fell easy to solve
[03:20.23]But an obtuse triange gonna make you feel confused
[03:22.26]Don't worry about what you do
[03:23.64]There are always means to solve
[03:24.80]As long as you master the sine cosine law
[03:30.04]At this moment I've got nothing to say
[03:33.80]As trig-functions rain down upon me
[03:38.45]At this  moment I've got nothing to say
[03:42.52]Let's sing a song about trig-functions
[03:47.13]Long live the trigonometric functions
[03:55.85]