trigonometric functions

trigonometric functions 歌词

歌曲 trigonometric functions
歌手 天儿
专辑 科学狂想曲
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[00:00.00] 作曲 : 天儿
[00:01.00] 作词 : 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 sine curve,I'd be your cosine curve
[01:25.73] I'll be your derivative,you'll be my negtive 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 sovle
[03:20.23] But an obtuse triange's 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 momnet I've got nothing to say
[03:33.80] As trig-functions rain down upon me
[03:38.45] At this momnet I've got nothing to say
[03:42.52] Let's sing a song about trig-functios
[03:47.13] Long live the trigonometric functions
[03:55.85]
[00:00.00] zuo qu : tian r
[00:01.00] zuo ci : tian r
[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 trigfunctions
[00:25.82] sin 2 sin
[00:27.94] cos 2 cos
[00:29.89] tan 2 tan
[00:31.83] which is induction formula1, and induction formula 2
[00:34.23] sin sin
[00:36.35] cos cos
[00:38.63] tan tan
[00:40.69] sin sin
[00:42.53] cos cos
[00:44.99] tan tan
[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 2 cos
[00:53.48] sin 2 cos
[00:55.45] cos 2 sin
[00:57.84] cos 2 sin
[00:59.92] tan 2 cot
[01:01.77] tan 2 cot
[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 sine curve, I' d be your cosine curve
[01:25.73] I' ll be your derivative, you' ll be my negtive 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 sin cos cos sin
[02:58.94] cos cos cos sin sin
[03:02.22] tan tan tan 1tan tan
[03:06.25] sin sin cos cos sin
[03:09.59] cos cos cos sin sin
[03:12.93] tan tan tan 1 tan tan
[03:17.99] As you come across a right triangle you fell easy to sovle
[03:20.23] But an obtuse triange' s 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 momnet I' ve got nothing to say
[03:33.80] As trigfunctions rain down upon me
[03:38.45] At this momnet I' ve got nothing to say
[03:42.52] Let' s sing a song about trigfunctios
[03:47.13] Long live the trigonometric functions
[03:55.85]
[00:00.00] zuò qǔ : tiān r
[00:01.00] zuò cí : tiān r
[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 trigfunctions
[00:25.82] sin 2 sin
[00:27.94] cos 2 cos
[00:29.89] tan 2 tan
[00:31.83] which is induction formula1, and induction formula 2
[00:34.23] sin sin
[00:36.35] cos cos
[00:38.63] tan tan
[00:40.69] sin sin
[00:42.53] cos cos
[00:44.99] tan tan
[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 2 cos
[00:53.48] sin 2 cos
[00:55.45] cos 2 sin
[00:57.84] cos 2 sin
[00:59.92] tan 2 cot
[01:01.77] tan 2 cot
[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 sine curve, I' d be your cosine curve
[01:25.73] I' ll be your derivative, you' ll be my negtive 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 sin cos cos sin
[02:58.94] cos cos cos sin sin
[03:02.22] tan tan tan 1tan tan
[03:06.25] sin sin cos cos sin
[03:09.59] cos cos cos sin sin
[03:12.93] tan tan tan 1 tan tan
[03:17.99] As you come across a right triangle you fell easy to sovle
[03:20.23] But an obtuse triange' s 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 momnet I' ve got nothing to say
[03:33.80] As trigfunctions rain down upon me
[03:38.45] At this momnet I' ve got nothing to say
[03:42.52] Let' s sing a song about trigfunctios
[03:47.13] Long live the trigonometric functions
[03:55.85]
[00:10.56] 当你初学数学中的1234
[00:11.80] 当你初学数学中的1234
[00:12.88] 初学方程中的XYZT
[00:13.97] 初学方程中的XYZT
[00:14.94] 它将帮助你进行逻辑思考
[00:16.11] 它将帮助你进行逻辑思考
[00:16.96] 当你唱起正弦,余弦,余弦,正切
[00:18.27] 当你唱起正弦,余弦,余弦,正切
[00:19.28] 正弦,余弦,正切,余切
[00:20.25] 正弦,余弦,正切,余切
[00:21.40] 正弦,余弦,正割,余割
[00:22.34] 正弦,余弦,正割,余割
[00:23.57] 让我们唱起三角函数的歌谣吧
[00:24.54] 让我们唱起三角函数的歌谣吧
[00:25.25] 诱导公式
[00:25.82] sin(2π+α)=sinα
[00:27.94] cos(2π+α)=cosα
[00:29.89] tan(2π+α)=tanα
[00:31.83] 这是诱导公式归类1,下面是诱导公式归类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] 这些均为“函数名不变”
[00:48.56] 这些均为“函数名不变”
[00:49.29] 当π成为π/2是变化会很大
[00:50.32] 当π成为π/2是变化会很大
[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] 这就是说 :奇变偶不变
[01:13.47] 符号看象限
[01:14.92] 这就是说 “奇变偶不变,符号看象限 ”
[01:17.08] 但不论你在哪
[01:18.37] 但不论你在哪
[01:19.16] 我将会说
[01:20.24] 我将会说
[01:21.49] 你若为正弦曲线,我愿做余弦曲线
[01:22.65] 你若为正弦曲线,我愿做余弦曲线
[01:25.73] 我将为你的导数,你将为我负导数
[01:26.94] 我将为你的导数,你将为我负导数
[01:29.76] 当你改变振幅,我改变相位
[01:32.08] 当你改变振幅,我改变相位
[01:34.17] 我们可在外界空间自由震荡
[01:36.35] 我们可在外界空间自由震荡
[01:38.44] 当我们改变周期和手边常数
[01:40.79] 当我们改变周期和手边常数
[01:42.61] 我们从原点驶向无尽
[01:44.98] 我们从原点驶向无尽
[01:46.85] 是你,正弦,余弦
[01:48.80] 是你,正弦,余弦
[01:51.27] 创造了世间动人的音乐
[01:54.37] 创造了世间动人的音乐
[01:55.45] 是你,正切,余切
[01:57.46] 是你,正切,余切
[01:59.74] 揭示了中心对称的真谛
[02:01.02] 揭示了中心对称的真谛
[02:03.44] B BOX表演已开始
[02:46.93] 你想测量河宽及塔高
[02:48.26] 你想测量河宽及塔高
[02:49.27] 你抓耳挠腮一个多小时也想不出
[02:50.36] 你抓耳挠腮一个多小时也想不出
[02:51.40] 你无需向dalao们请教
[02:52.55] 你无需向dalao们请教
[02:53.49] 这一组公式将帮你解决
[02:54.52] 这一组公式将帮你解决
[02:55.50] 恒等变换
[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] 当你遇到直角三角形很容易解
[03:19.65] 当你遇到直角三角形很容易解
[03:20.23] 但钝角三角形使你感到困惑
[03:21.20] 但钝角三角形使你感到困惑
[03:22.26] 无须担心
[03:23.12] 无须担心
[03:23.64] 总有解决方法
[03:24.27] 总有解决方法
[03:24.80] 只要你掌握了正余弦定理
[03:25.68] 只要你掌握了正余弦定理
[03:30.04] 此刻我无以言表
[03:32.04] 此刻我无以言表
[03:33.80] 当时三角函数犹雨点般落向我
[03:36.11] 当时三角函数犹雨点般落向我
[03:38.45] 此刻我无以言表
[03:40.63] 此刻我无以言表
[03:42.52] 让我们唱起三角函数歌谣吧
[03:44.42] 让我们唱起三角函数歌谣吧
[03:47.13] 三角函数万岁
[03:50.32] 三角函数万岁
trigonometric functions 歌词
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