作词 : 天儿 作曲 : 天儿 when you first study math about 1234 first study equation about xyzt It will help you to think in a logical way When you sing sine, cosine, cosine, tangent Sine, cosine, tangent, cotangent Sine, cosine, ..., secant, cosecant Let's sing a song about trig-functions sin（2π+α）=sinα cos（2π+α）=cosα tan（2π+α）=tanα which is induction formula1, and induction formula 2 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 donot change" As pi goes to half pi the difference shall be huge sin（π/2+α）=cosα sin（π/2－α）=cosα cos（π/2+α）=－sinα cos（π/2－α）=sinα tan（π/2+α）=－cotα tan（π/2－α）=cotα That is to say the odds will change, evens are conserved The notations that they get depend on where they are But no matter where you are I've gotta say that If you were my sine curve, I'd be your cosine curve I'll be your derivative, you'll be my negative one As you change you amplitude, I change my phase We can oscillate freely in the external space As we change our period and costant at hand We travel from the origin to infinity It's you sine, and you cosine Who make charming music around the world It's you tangent, cotangent Who proclaim the true meaning of centrosymmetry B BOX You wanna measure width of a river, height of a tower You scratch your head which cost you more than an hour You don't need to ask any "gods" or" master" for help This group of formulas are gonna help you solve 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 But an obtuse triange gonna make you feel confused Don't worry about what you do There are always means to solve As long as you master the sine cosine law At this moment I've got nothing to say As trig-functions rain down upon me At this moment I've got nothing to say Let's sing a song about trig-functions Long live the trigonometric functions
[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]
