{"meta":{"N":"trigonometric functions","S":"天儿","LA":"天儿","MA":"天儿","C":"科学狂想曲","A":"3949AB","G1":"3949AB","G2":"1976D2","O":"https://music.163.com/#/song?id=34380194","P":"0501/avatar","X":"2F3FA1"},"lyrics":[{"id":-1,"type":"lyrics","ac":"--","n":"pre","premark":true,"display":true,"title":false,"in":[{"id":-1,"ts":"0","c":"- - - - - - -"}]},{"id":0,"type":"lyrics","ac":"N1","n":"段落1","display":true,"title":true,"in":[{"id":0,"ts":104,"c":"when you first study math about 1234"},{"id":1,"ts":1610612736,"c":"当你初学数学中的1234"},{"id":2,"ts":130,"c":"first study equation about xyzt"},{"id":3,"ts":1610612736,"c":"初学方程中的XYZT"},{"id":4,"ts":151,"c":"It will help you to think in a logical way"},{"id":5,"ts":1610612736,"c":"它将帮助你进行逻辑思考"},{"id":6,"ts":169,"c":"When you sing sine,cosine,cosine,tangent"},{"id":7,"ts":1610612736,"c":"当你唱起正弦,余弦,余弦,正切"},{"id":8,"ts":192,"c":"Sine,cosine,tangent,cotangent"},{"id":9,"ts":1610612736,"c":"正弦,余弦,正切,余切"},{"id":10,"ts":213,"c":"Sine,cosine,..,secant,cosecant"},{"id":11,"ts":1610612736,"c":"正弦,余弦,正割,余割"},{"id":12,"ts":235,"c":"Let's sing a song about trig-functions"},{"id":13,"ts":1610612736,"c":"让我们唱起三角函数的歌谣吧"}]},{"id":1,"type":"lyrics","ac":"N2","n":"段落2","display":true,"title":true,"in":[{"id":14,"ts":260,"c":"sin(2π+α) = sinα"},{"id":15,"ts":1610612736,"c":"sin(2π+α) = sinα"},{"id":16,"ts":278,"c":"cos(2π+α) = cosα"},{"id":17,"ts":1610612736,"c":"cos(2π+α) = cosα"},{"id":18,"ts":299,"c":"tan(2π+α) = tanα"},{"id":19,"ts":1610612736,"c":"tan(2π+α) = tanα"},{"id":20,"ts":320,"c":"which is induction formula1,and induction formula 2"},{"id":21,"ts":1610612736,"c":"这是诱导公式归类1,下面是诱导公式归类2"},{"id":22,"ts":342,"c":"sin(π+α) = -sinα"},{"id":23,"ts":1610612736,"c":"sin(π+α) = -sinα"},{"id":24,"ts":366,"c":"cos(π+α) = -cosα"},{"id":25,"ts":1610612736,"c":"cos(π+α) = -cosα"},{"id":26,"ts":387,"c":"tan(π+α) = tanα"},{"id":27,"ts":1610612736,"c":"tan(π+α) = tanα"},{"id":28,"ts":406,"c":"sin(π-α) = sinα"},{"id":29,"ts":1610612736,"c":"sin(π-α) = sinα"},{"id":30,"ts":427,"c":"cos(π-α) = -cosα"},{"id":31,"ts":1610612736,"c":"cos(π-α) = -cosα"},{"id":32,"ts":450,"c":"tan(π-α) = -tanα"},{"id":33,"ts":1610612736,"c":"tan(π-α) = -tanα"},{"id":34,"ts":470,"c":"These are all those \"name donot -change\""},{"id":35,"ts":1610612736,"c":"这些均为“函数名不变”"}]},{"id":2,"type":"lyrics","ac":"N3","n":"段落3","display":true,"title":true,"in":[{"id":36,"ts":493,"c":"As pi goes to half pi the difference shall be huge"},{"id":37,"ts":1610612736,"c":"当π成为π/2是变化会很大"},{"id":38,"ts":515,"c":"sin(π/2+α) = cosα"},{"id":39,"ts":1610612736,"c":"sin(π/2+α) = cosα"},{"id":40,"ts":534,"c":"cos(π/2-α) = sinα"},{"id":41,"ts":1610612736,"c":"cos(π/2-α) = sinα"},{"id":42,"ts":555,"c":"sin(π/2-α) = cosα"},{"id":43,"ts":1610612736,"c":"sin(π/2-α) = cosα"},{"id":44,"ts":577,"c":"cos(π/2+α) = -sinα"},{"id":45,"ts":1610612736,"c":"cos(π/2+α) = -sinα"},{"id":46,"ts":599,"c":"tan(π/2+α) = -cotα"},{"id":47,"ts":1610612736,"c":"tan(π/2+α) = -cotα"},{"id":48,"ts":621,"c":"tan(π/2-α) = cotα"},{"id":49,"ts":1610612736,"c":"tan(π/2-α) = cotα"}]},{"id":3,"type":"lyrics","ac":"N4","n":"段落4","display":true,"title":true,"in":[{"id":50,"ts":684,"c":"That is to say the odds will change, evens are conserved"},{"id":51,"ts":1610612736,"c":"这就是说 :奇变偶不变"},{"id":52,"ts":727,"c":"The notations that they get depend on where they are"},{"id":53,"ts":1610612736,"c":"符号看象限"},{"id":54,"ts":767,"c":"But no matter where you are, I've gotta say that"},{"id":55,"ts":1610612736,"c":"但不论你在哪,我将会说"},{"id":56,"ts":813,"c":"If you were my sine curve,I'd be your cosine curve"},{"id":57,"ts":1610612736,"c":"你若为正弦曲线,我愿做余弦曲线"},{"id":58,"ts":858,"c":"I'll be your derivative,you'll be my negtive one"},{"id":59,"ts":1610612736,"c":"我将为你的导数,你将为我负导数"},{"id":60,"ts":898,"c":"As you change you amplitude,I change my phase"},{"id":61,"ts":1610612736,"c":"当你改变振幅,我改变相位"},{"id":62,"ts":939,"c":"We can oscillate freely in the external space"},{"id":63,"ts":1610612736,"c":"我们可在外界空间自由震荡"},{"id":64,"ts":984,"c":"As we change our period and costant at hand"},{"id":65,"ts":1610612736,"c":"当我们改变周期和手边常数"},{"id":66,"ts":1025,"c":"We travel from the origin to infinity"},{"id":67,"ts":1610612736,"c":"我们从原点驶向无尽"}]},{"id":4,"type":"lyrics","ac":"N5","n":"段落5","display":true,"title":true,"in":[{"id":68,"ts":1067,"c":"It's you sine,and you cosine"},{"id":69,"ts":1610612736,"c":"是你,正弦,余弦"},{"id":70,"ts":1111,"c":"Who make charming music around the world"},{"id":71,"ts":1610612736,"c":"创造了世间动人的音乐"},{"id":72,"ts":1153,"c":"It's you tangent,cotangent"},{"id":73,"ts":1610612736,"c":"是你,正切,余切"},{"id":74,"ts":1195,"c":"Who proclaim the true meaning of centrosymmetry"},{"id":75,"ts":1610612736,"c":"揭示了中心对称的真谛"}]},{"id":5,"type":"lyrics","ac":"--","n":"间奏","display":true,"title":true,"in":[{"id":76,"ts":1242,"c":"- - - - - - -"}]},{"id":6,"type":"lyrics","ac":"N6","n":"段落6","display":true,"title":true,"in":[{"id":77,"ts":1667,"c":"You wanna measure width of a river,height of a tower"},{"id":78,"ts":1610612736,"c":"你想测量河宽及塔高"},{"id":79,"ts":1692,"c":"You scratch your head which cost you more than an hour"},{"id":80,"ts":1610612736,"c":"你抓耳挠腮一个多小时也想不出"},{"id":81,"ts":1712,"c":"You don't need to ask any \"gods\" or \"master\" for help"},{"id":82,"ts":1610612736,"c":"你无需向dalao们请教"},{"id":83,"ts":1735,"c":"This group of formulas are gonna help you solve"},{"id":84,"ts":1610612736,"c":"这一组公式将帮你解决"},{"id":85,"ts":1756,"c":"sin(α+β) = sinα•cosβ + cosα•sinβ"},{"id":86,"ts":1610612736,"c":"sin(α+β) = sinα•cosβ + cosα•sinβ"},{"id":87,"ts":1790,"c":"cos(α+β) = cosα•cosβ - sinα•sinβ"},{"id":88,"ts":1610612736,"c":"cos(α+β) = cosα•cosβ - sinα•sinβ"},{"id":89,"ts":1822,"c":"tan(α+β) = (tanα + tanβ) / (1 - tanα•tanβ)"},{"id":90,"ts":1610612736,"c":"tan(α+β) = (tanα + tanβ) / (1 - tanα•tanβ)"},{"id":91,"ts":1860,"c":"sin(α-β) = sinα•cosβ - cosα•sinβ"},{"id":92,"ts":1610612736,"c":"sin(α-β) = sinα•cosβ - cosα•sinβ"},{"id":93,"ts":1898,"c":"cos(α-β) = cosα•cosβ + sinα•sinβ"},{"id":94,"ts":1610612736,"c":"cos(α-β) = cosα•cosβ + sinα•sinβ"},{"id":95,"ts":1929,"c":"tan(α-β) = (tanα - tanβ) / (1 + tanα•tanβ)"},{"id":96,"ts":1610612736,"c":"tan(α-β) = (tanα - tanβ)/(1 + tanα•tanβ)"},{"id":97,"ts":1978,"c":"As you come across a right triangle you fell easy to sovle"},{"id":98,"ts":1610612736,"c":"当你遇到直角三角形很容易解"},{"id":99,"ts":2003,"c":"But an obtuse triange's gonna make you feel confused"},{"id":100,"ts":1610612736,"c":"但钝角三角形使你感到困惑"},{"id":101,"ts":2025,"c":"Don't worry about what you do"},{"id":102,"ts":1610612736,"c":"无须担心"},{"id":103,"ts":2038,"c":"There are always means to solve"},{"id":104,"ts":1610612736,"c":"总有解决方法"},{"id":105,"ts":2047,"c":"As long as you master the sine cosine law"},{"id":106,"ts":1610612736,"c":"只要你掌握了正余弦定理"}]},{"id":7,"type":"lyrics","ac":"N7","n":"段落7","display":true,"title":true,"in":[{"id":107,"ts":2096,"c":"At this momnet I've got nothing to say"},{"id":108,"ts":1610612736,"c":"此刻我无以言表"},{"id":109,"ts":2139,"c":"As trig-functions rain down upon me"},{"id":110,"ts":1610612736,"c":"当时三角函数犹雨点般落向我"},{"id":111,"ts":2184,"c":"At this moment I've got nothing to say"},{"id":112,"ts":1610612736,"c":"此刻我无以言表"},{"id":113,"ts":2225,"c":"Let's sing a song about trig-functions"},{"id":114,"ts":1610612736,"c":"让我们唱起三角函数歌谣吧"},{"id":115,"ts":2267,"c":"Long live the trigonometric functions"},{"id":116,"ts":1610612736,"c":"三角函数万岁"}]},{"id":8,"type":"final","ts":2335,"display":false}],"timestamps":{"0":[-1,-1],"104":[0,0],"1610612736":[7,116],"130":[0,2],"151":[0,4],"169":[0,6],"192":[0,8],"213":[0,10],"235":[0,12],"260":[1,14],"278":[1,16],"299":[1,18],"320":[1,20],"342":[1,22],"366":[1,24],"387":[1,26],"406":[1,28],"427":[1,30],"450":[1,32],"470":[1,34],"493":[2,36],"515":[2,38],"534":[2,40],"555":[2,42],"577":[2,44],"599":[2,46],"621":[2,48],"684":[3,50],"727":[3,52],"767":[3,54],"813":[3,56],"858":[3,58],"898":[3,60],"939":[3,62],"984":[3,64],"1025":[3,66],"1067":[4,68],"1111":[4,70],"1153":[4,72],"1195":[4,74],"1242":[5,76],"1667":[6,77],"1692":[6,79],"1712":[6,81],"1735":[6,83],"1756":[6,85],"1790":[6,87],"1822":[6,89],"1860":[6,91],"1898":[6,93],"1929":[6,95],"1978":[6,97],"2003":[6,99],"2025":[6,101],"2038":[6,103],"2047":[6,105],"2096":[7,107],"2139":[7,109],"2184":[7,111],"2225":[7,113],"2267":[7,115],"2335":[-2,-2]}} --------TxmpSwitchDataBoundary-------- {"baseurl":"https://music-archive.sparkslab.art/0501","song_id":"0501","src1":"https://music-archive.sparkslab.art/0501/audio.mp3","src2":"https://music-archive.sparkslab.art/0501/background","cover":"https://music-archive.sparkslab.art/0501/avatar","player_colored_css":"https://music-archive.sparkslab.art/dynamic/css/player/player-colored.css?v=129a&w=&A=X3949AB&S=X2F3FA1&G1=X3949AB&G2=X1976D2","main_colored_css":"https://music-archive.sparkslab.art/dynamic/css/common/main-colored.css?v=129a&w=&A=X3949AB&S=X2F3FA1&G1=X3949AB&G2=X1976D2","title":"Player ‹ trigonometric functions - Music Archive","source":"internal","payment":{"no_play":false,"no_download":false,"pay_play":false,"pay_download":false},"meta":{"N":"trigonometric functions","S":"天儿","LA":"天儿","MA":"天儿","C":"科学狂想曲","A":"3949AB","G1":"3949AB","G2":"1976D2","O":"https://music.163.com/#/song?id=34380194","P":"0501/avatar","X":"2F3FA1"},"modified":1630330946,"audio_info":{"format":"mp3","bitrate":192,"time":242}} --------TxmpSwitchDataBoundary--------
0trigonometric functions
天儿
[段落1 N1]
1when you first study math about 1234
~当你初学数学中的1234
2first study equation about xyzt
~初学方程中的XYZT
3It will help you to think in a logical way
~它将帮助你进行逻辑思考
4When you sing sine,cosine,cosine,tangent
~当你唱起正弦,余弦,余弦,正切
5Sine,cosine,tangent,cotangent
~正弦,余弦,正切,余切
6Sine,cosine,..,secant,cosecant
~正弦,余弦,正割,余割
7Let's sing a song about trig-functions
~让我们唱起三角函数的歌谣吧
[段落2 N2]
8sin(2π+α) = sinα
~sin(2π+α) = sinα
9cos(2π+α) = cosα
~cos(2π+α) = cosα
10tan(2π+α) = tanα
~tan(2π+α) = tanα
11which is induction formula1,and induction formula 2
~这是诱导公式归类1,下面是诱导公式归类2
12sin(π+α) = -sinα
~sin(π+α) = -sinα
13cos(π+α) = -cosα
~cos(π+α) = -cosα
14tan(π+α) = tanα
~tan(π+α) = tanα
15sin(π-α) = sinα
~sin(π-α) = sinα
16cos(π-α) = -cosα
~cos(π-α) = -cosα
17tan(π-α) = -tanα
~tan(π-α) = -tanα
18These are all those "name donot -change"
~这些均为“函数名不变”
[段落3 N3]
19As pi goes to half pi the difference shall be huge
~当π成为π/2是变化会很大
20sin(π/2+α) = cosα
~sin(π/2+α) = cosα
21cos(π/2-α) = sinα
~cos(π/2-α) = sinα
22sin(π/2-α) = cosα
~sin(π/2-α) = cosα
23cos(π/2+α) = -sinα
~cos(π/2+α) = -sinα
24tan(π/2+α) = -cotα
~tan(π/2+α) = -cotα
25tan(π/2-α) = cotα
~tan(π/2-α) = cotα
[段落4 N4]
26That is to say the odds will change, evens are conserved
~这就是说 :奇变偶不变
27The notations that they get depend on where they are
~符号看象限
28But no matter where you are, I've gotta say that
~但不论你在哪,我将会说
29If you were my sine curve,I'd be your cosine curve
~你若为正弦曲线,我愿做余弦曲线
30I'll be your derivative,you'll be my negtive one
~我将为你的导数,你将为我负导数
31As you change you amplitude,I change my phase
~当你改变振幅,我改变相位
32We can oscillate freely in the external space
~我们可在外界空间自由震荡
33As we change our period and costant at hand
~当我们改变周期和手边常数
34We travel from the origin to infinity
~我们从原点驶向无尽
[段落5 N5]
35It's you sine,and you cosine
~是你,正弦,余弦
36Who make charming music around the world
~创造了世间动人的音乐
37It's you tangent,cotangent
~是你,正切,余切
38Who proclaim the true meaning of centrosymmetry
~揭示了中心对称的真谛
[间奏 --]
39- - - - - - -
[段落6 N6]
40You wanna measure width of a river,height of a tower
~你想测量河宽及塔高
41You scratch your head which cost you more than an hour
~你抓耳挠腮一个多小时也想不出
42You don't need to ask any "gods" or "master" for help
~你无需向dalao们请教
43This group of formulas are gonna help you solve
~这一组公式将帮你解决
44sin(α+β) = sinα•cosβ + cosα•sinβ
~sin(α+β) = sinα•cosβ + cosα•sinβ
45cos(α+β) = cosα•cosβ - sinα•sinβ
~cos(α+β) = cosα•cosβ - sinα•sinβ
46tan(α+β) = (tanα + tanβ) / (1 - tanα•tanβ)
~tan(α+β) = (tanα + tanβ) / (1 - tanα•tanβ)
47sin(α-β) = sinα•cosβ - cosα•sinβ
~sin(α-β) = sinα•cosβ - cosα•sinβ
48cos(α-β) = cosα•cosβ + sinα•sinβ
~cos(α-β) = cosα•cosβ + sinα•sinβ
49tan(α-β) = (tanα - tanβ) / (1 + tanα•tanβ)
~tan(α-β) = (tanα - tanβ)/(1 + tanα•tanβ)
50As you come across a right triangle you fell easy to sovle
~当你遇到直角三角形很容易解
51But an obtuse triange's gonna make you feel confused
~但钝角三角形使你感到困惑
52Don't worry about what you do
~无须担心
53There are always means to solve
~总有解决方法
54As long as you master the sine cosine law
~只要你掌握了正余弦定理
[段落7 N7]
55At this momnet I've got nothing to say
~此刻我无以言表
56As trig-functions rain down upon me
~当时三角函数犹雨点般落向我
57At this moment I've got nothing to say
~此刻我无以言表
58Let's sing a song about trig-functions
~让我们唱起三角函数歌谣吧
59Long live the trigonometric functions
~三角函数万岁