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作曲 : 天儿 |
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作词 : 天儿 |
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when you first study math about 1234 |
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first study equation about xyzt |
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It will help you to think in a logical way |
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When you sing sine,cosine,cosine,tangent |
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Sine,cosine,tangent,cotangent |
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Sine,cosine,..,secant,cosecant |
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Let's sing a song about trig-functions |
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sin（2π+α）=sinα |
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cos（2π+α）=cosα |
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tan（2π+α）=tanα |
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which is induction formula1,and induction formula 2 |
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sin（π+α）= —sinα |
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cos（π+α）=—cosα |
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tan（π+α）= tanα |
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sin（π－α）= sinα |
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cos（π－α）=－cosα |
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tan（π－α）=－tanα |
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These are all those "name donot -change" |
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As pi goes to half pi the difference shall be huge |
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sin（π/2+α）=cosα |
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sin（π/2－α）=cosα |
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cos（π/2+α）=－sinα |
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cos（π/2－α）=sinα |
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tan（π/2+α）=－cotα |
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tan（π/2－α）=cotα |
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That is to say the odds will change,evens are conserved |
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The notations that they get depend on where they are |
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But no matter where you are |
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I‘ve gotta say that |
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If you were sine curve,I'd be your cosine curve |
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I'll be your derivative,you'll be my negtive one |
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As you change you amplitude,I change my phase |
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We can oscillate freely in the external space |
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As we change our period and costant at hand |
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We travel from the origin to infinity |
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It's you sine,and you cosine |
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Who make charming music around the world |
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It's you tangent,cotangent |
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Who proclaim the true meaning of centrosymmetry |
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B BOX |
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You wanna measure width of a river,height of a tower |
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You scratch your head which cost you more than an hour |
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You don't need to ask any "gods" or" master" for help |
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This group of formulas are gonna help you solve |
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sin(α+β)=sinα•cosβ+cosα•sinβ |
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cos(α+β)=cosα•cosβ-sinα•sinβ |
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tan(α+β)=(tanα+tanβ)/(1-tanα•tanβ) |
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sin(α-β)=sinα•cosβ-cosα•sinβ |
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cos(α-β)=cosα•cosβ+sinα•sinβ |
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tan(α-β)=(tanα-tanβ)/(1+tanα•tanβ) |
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As you come across a right triangle you fell easy to sovle |
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But an obtuse triange's gonna make you feel confused |
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Don't worry about what you do |
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There are always means to solve |
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As long as you master the sine cosine law |
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At this momnet I've got nothing to say |
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As trig-functions rain down upon me |
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At this momnet I've got nothing to say |
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Let's sing a song about trig-functios |
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Long live the trigonometric functions |
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