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trigonometric functions
天儿
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[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]
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