天儿――三角函数之歌

致: 不擅长英语的我们！ 00:10 when you first study math about 1234 当你初学数学中的1234 first study equation about xyzt 初学方程中的XYZT It will help you to think in a logical way 它将帮助你进行逻辑思考 When you sing sine,cosine,cosine,tangent 当你唱起正弦，余弦，余弦，正切 Sine,cosine,tangent,cotangent 正弦，余弦，正切，余切 Sine,cosine,..,secant,cosecant 正弦，余弦，正割，余割 Let's sing a song about trig-functions 让我们唱起三角函数的歌谣吧 诱导公式 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" 这些均为“函数名不变” As pi goes to half pi the difference shall be huge 当π成为π/2是变化会很大 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 这就是说“奇变偶不变 符号看象限” But no matter where you are 但不论你在哪 I‘ve gotta say that 我将会说 If you were sine curve,I'd be your cosine curve 你若为正弦曲线，我愿做余弦曲线 I'll be your derivative,you'll be my negtive one 我将为你的导数，你将为我负导数 As you change you amplitude,I change my phase 当你改变振幅，我改变相位 We can oscillate freely in the external space 我们可在外界空间自由震荡 As we change our period and costant at hand 当我们改变周期和手边常数 We travel from the origin to infinity 我们从原点驶向无穷远 It's you sine,and you cosine 是你，正弦，余弦 Who make charming music around the world 创造了世间动人的音乐 It's you tangent,cotangent 是你，正切，余切 Who proclaim the true meaning of centrosymmetry 揭示了中心对称的真谛 B BOX You wanna measure width of a river,height of a tower 你想测量河宽及塔高 You scratch your head which cost you more than an hour 你抓耳挠腮想不出 You don't need to ask any "gods" or" master" for help 你无需向大神们请教 This group of formulas are gonna help you solve 这一组公式将帮你解决 恒等变换 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 sovle 当你遇到直角三角形很容易解 But an obtuse triange's gonna make you feel confused 但钝角三角形使你困惑 Don't worry about what you do 无须担心 There are always means to solve 总有解决方法 As long as you master the sine cosine law 只要你掌握了正余弦定理 At this momnet I've got nothing to say 此刻我无以言表 As trig-functions rain down upon me 当时三角函数犹雨点般落向我 At this momnet I've got nothing to say 此刻我无以言表 Let's sing a song about trig-functios 让我们唱起三角函数歌谣吧 Long live the trigonometric functions 三角函数万岁