[00:01.007]原唱：映射者/天儿

[00:04.183]翻唱：讲不清

[00:06.429]后期：昔染

[00:08.518]视频：讲不清

[00:09.168]

[00:10.560]when you first study math about 1234

[00:12.880]first study equation about xyzt

[00:14.940]It will help you to think in a logical way

[00:16.960]When you sing sine, cosine, cosine, tangent

[00:19.280]Sine, cosine, tangent, cotangent

[00:21.400]Sine, cosine, ..., secant, cosecant

[00:23.570]Let's sing a song about trig-functions

[00:25.820]sin（2π+α）=sinα

[00:27.940]cos（2π+α）=cosα

[00:29.890]tan（2π+α）=tanα

[00:31.830]which is induction formula1, and induction formula 2

[00:34.230]sin（π+α）= —sinα

[00:36.350]cos（π+α）=—cosα

[00:38.630]tan（π+α）= tanα

[00:40.690]sin（π－α）= sinα

[00:42.530]cos（π－α）=－cosα

[00:44.990]tan（π－α）=－tanα

[00:47.110]These are all those "name donot change"

[00:49.290]As pi goes to half pi the difference shall be huge

[00:51.360]sin（π/2+α）=cosα

[00:53.480]sin（π/2－α）=cosα

[00:55.450]cos（π/2+α）=－sinα

[00:57.840]cos（π/2－α）=sinα

[00:59.920]tan（π/2+α）=－cotα

[01:01.770]tan（π/2－α）=cotα

[01:08.600]That is to say the odds will change, evens are conserved

[01:13.470]The notations that they get depend on where they are

[01:17.080]But no matter where you are

[01:19.160]I've gotta say that

[01:21.490]If you were my sine curve, I'd be your cosine curve

[01:25.730]I'll be your derivative, you'll be my negative one

[01:29.760]As you change you amplitude, I change my phase

[01:34.170]We can oscillate freely in the external space

[01:38.440]As we change our period and costant at hand

[01:42.610]We travel from the origin to infinity

[01:46.850]It's you sine, and you cosine

[01:51.270]Who make charming music around the world

[01:55.450]It's you tangent, cotangent

[01:59.740]Who proclaim the true meaning of centrosymmetry

[02:03.440]No B BOX

[02:46.930]You wanna measure width of a river, height of a tower

[02:49.270]You scratch your head which cost you more than an hour

[02:51.400]You don't need to ask any "gods" or" master" for help

[02:53.490]This group of formulas are gonna help you solve

[02:55.820]sin(α+β)=sinα•cosβ+cosα•sinβ

[02:58.940]cos(α+β)=cosα•cosβ-sinα•sinβ

[03:02.220]tan(α+β)=(tanα+tanβ)/(1-tanα•tanβ)

[03:06.250]sin(α-β)=sinα•cosβ-cosα•sinβ

[03:09.590]cos(α-β)=cosα•cosβ+sinα•sinβ

[03:12.930]tan(α-β)=(tanα-tanβ)/(1+tanα•tanβ)

[03:17.990]As you come across a right triangle you fell easy to solve

[03:20.230]But an obtuse triange gonna make you feel confused

[03:22.260]Don't worry about what you do

[03:23.640]There are always means to solve

[03:24.800]As long as you master the sine cosine law

[03:30.040]At this moment I've got nothing to say

[03:33.800]As trig-functions rain down upon me

[03:38.450]At this moment I've got nothing to say

[03:42.520]Let's sing a song about trig-functions

[03:47.130]Long live the trigonometric functions

[03:55.850]