trigonometric functions - 天儿

[00:00.01]trigonometric functions - 天儿
[00:03.83]作词：天儿 作曲：天儿
[00:10.86]when you first study math about 1234
[00:12.74]first study equation about xyzt
[00:14.93]It will help you to think in a logical way
[00:16.97]When you sing sine cosine cosine tangent
[00:19.34]Sine cosine tangent cotangent
[00:21.43]Sine cosine .. secant cosecant
[00:24.6]Let's sing a song about trig-functions
[00:26.3]sin（2π+α）=sinα
[00:27.64]cos（2π+α）=cosα
[00:29.96]tan（2π+α）=tanα
[00:32.02]which is induction formula1 and induction formula 2
[00:34.3]sin（π+α）= -sinα
[00:36.43]cos（π+α）=-cosα
[00:38.55]tan（π+α）= tanα
[00:40.53]sin（π－α）= sinα
[00:42.72]cos（π－α）=－cosα
[00:44.79]tan（π－α）=－tanα
[00:47.27]These are all those name donot -change
[00:49.24]As pi goes to half pi the difference shall be huge
[00:51.71]sin（π/2+α）=cosα
[00:53.36]sin（π/2－α）=cosα
[00:55.55]cos（π/2+α）=－sinα
[00:58.08]cos（π/2－α）=sinα
[00:59.83]tan（π/2+α）=－cotα
[01:01.88]tan（π/2－α）=cotα
[01:08.93]That is to say the odds will change evens are conserved
[01:12.71]The notations that they get depend on where they are
[01:16.87]But no matter where you are
[01:19.12]I've gotta say that
[01:21.229996]If you were sine curve I'd be your cosine curve
[01:25.71]I'll be your derivative you'll be my negtive one
[01:30.0]As you change you amplitude I change my phase
[01:34.11]We can oscillate freely in the external space
[01:38.41]As we change our period and costant at hand
[01:42.8]We travel from the origin to infinity
[01:47.130005]It's you sine and you cosine
[01:51.29]Who make charming music around the world
[01:55.56]It's you tangent cotangent
[01:57.89]Who proclaim the true meaning of centrosymmetry
[02:47.29001]You wanna measure width of a river height of a tower
[02:49.37]You scratch your head which cost you more than an hour
[02:51.41]You don't need to ask any "gods" or" master" for help
[02:53.62]This group of formulas are gonna help you solve
[02:55.86]sin(α+β)=sinα?cosβ+cosα?sinβ
[02:59.06]cos(α+β)=cosα?cosβ-sinα?sinβ
[03:02.17]tan(α+β)=(tanα+tanβ)/(1-tanα?tanβ)
[03:06.49]sin(α-β)=sinα?cosβ-cosα?sinβ
[03:09.74]cos(α-β)=cosα?cosβ+sinα?sinβ
[03:12.91]tan(α-β)=(tanα-tanβ)/(1+tanα?tanβ)
[03:18.1]As you come across a right triangle you fell easy to sovle
[03:20.39]But an obtuse triange's gonna make you feel confused
[03:22.55]Don't worry about what you do
[03:23.8]There are always means to solve
[03:25.01]As long as you master the sine cosine law
[03:30.26]At this momnet I've got nothing to say
[03:34.01]As trig-functions rain down upon me
[03:38.43]At this momnet I've got nothing to say
[03:42.67]Let's sing a song about trig-functios
[03:47.05]Long live the trigonometric functions