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- - - - -"}]},{"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.sparks-lab.art/0501","song_id":"0501","src1":"https://music-archive.sparks-lab.art/0501/audio.mp3","src2":"https://music-archive.sparks-lab.art/0501/background","cover":"https://music-archive.sparks-lab.art/0501/avatar","player_colored_css":"https://music-archive.sparks-lab.art/dynamic/css/player/player-colored.css?v=129a-pre4&w=&A=X3949AB&S=X2F3FA1&G1=X3949AB&G2=X1976D2","main_colored_css":"https://music-archive.sparks-lab.art/dynamic/css/common/main-colored.css?v=129a-pre4&w=&A=X3949AB&S=X2F3FA1&G1=X3949AB&G2=X1976D2","title":"Player ‹ trigonometric functions - 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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

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trigonometric functions
0501

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