trigonometric functions-天儿
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[ti:trigonometric functions]
[ar:天儿]
[al:科学狂想曲]
[by:]
[offset:0]
[00:00.00]trigonometric functions - 天儿
[00:02.26]词：天儿
[00:03.09]曲：天儿
[00:03.89]
[00:10.60]When you first study math about 1234
[00:12.91]First study equation about xyzt
[00:14.83]It will help you to think in a logical way
[00:16.90]When you sing sine cosine cosine tangent
[00:19.33]Sine cosine tangent cotangent
[00:21.48]Sine cosine secant cosecant
[00:23.61]Let's sing a song about trig-functions
[00:25.72]sin(2π+α)=sinα
[00:27.87]cos(2π+α)=cosα
[00:30.02]tan(2π+α)=tanα
[00:31.92]Which is induction formula1 and induction formula 2
[00:34.30]sin(π+α)= -sinα
[00:36.46]cos(π+α)=-cosα
[00:38.66]tan(π+α)= tanα
[00:40.69]sin(π-α)= sinα
[00:42.85]cos(π-α)=-cosα
[00:45.02]tan(π-α)=-tanα
[00:47.22]These are all those"name do not -change"
[00:49.21]As pi goes to half pi the difference shall be huge
[00:51.69]sin(π/2+α)=cosα
[00:53.71]cos(π/2+α)=-sinα
[00:55.76]tan(π/2+α)=-cotα
[00:57.59]
[00:58.11]sin(π/2-α)=cosα
[01:00.00]cos(π/2-α)=sinα
[01:02.14]tan(π/2-α)=cotα
[01:04.04]
[01:08.80]That is to say the odds will change evens are conserved
[01:12.70]The notations that they get depend on where they are
[01:16.97]But no matter where you are
[01:19.36]I've gotta say that
[01:21.47]If you were my sine curve I'd be your cosine curve
[01:25.78]I'll be your derivative you'll be my negative one
[01:30.09]As you change you amplitude I change my phase
[01:33.98]We can oscillate freely in the external space
[01:37.96]
[01:38.54]As we change our period and costant at hand
[01:42.61]We travel from the origin to infinity
[01:46.54]
[01:47.16]It's you sine and you cosine
[01:51.46]Who make charming music around the world
[01:55.55]It's you tangent cotangent
[01:59.76]Who proclaim the true meaning of centrosymmetry
[02:03.62]
[02:47.09]You wanna measure width of a river height of a tower
[02:49.42]You scratch your head which cost you more than an hour
[02:51.45]You don't need to ask any"gods" or" master" for help
[02:53.62]This group of formulas are gonna help you solve
[02:55.75]sin(α+β)=sinα•cosβ+cosα•sinβ
[02:59.00]cos(α+β)=cosα•cosβ-sinα•sinβ
[03:02.32]tan(α+β)=(tanα+tanβ)/(1-tanα•tanβ)
[03:05.49]
[03:06.45]sin(α-β)=sinα•cosβ-cosα•sinβ
[03:09.80]cos(α-β)=cosα•cosβ+sinα•sinβ
[03:12.93]tan(α-β)=(tanα-tanβ)/(1+tanα•tanβ)
[03:18.10]As you come across a right triangle you fell easy to solve
[03:20.41]But an obtuse triangle gonna make you feel confused
[03:22.52]Don't worry about what you do
[03:23.65]There are always means to solve
[03:24.70]As long as you master the sine cosine law
[03:26.68]
[03:30.25]At this moment I've got nothing to say
[03:33.62]
[03:34.14]As trig-functions rain down upon me
[03:37.98]
[03:38.69]At this moment I've got nothing to say
[03:42.65]Let's sing a song about trig-functions
[03:46.68]
[03:47.22]Long live the trigonometric functions
[ar:天儿]
[al:科学狂想曲]
[by:]
[offset:0]
[00:00.00]trigonometric functions - 天儿
[00:02.26]词：天儿
[00:03.09]曲：天儿
[00:03.89]
[00:10.60]When you first study math about 1234
[00:12.91]First study equation about xyzt
[00:14.83]It will help you to think in a logical way
[00:16.90]When you sing sine cosine cosine tangent
[00:19.33]Sine cosine tangent cotangent
[00:21.48]Sine cosine secant cosecant
[00:23.61]Let's sing a song about trig-functions
[00:25.72]sin(2π+α)=sinα
[00:27.87]cos(2π+α)=cosα
[00:30.02]tan(2π+α)=tanα
[00:31.92]Which is induction formula1 and induction formula 2
[00:34.30]sin(π+α)= -sinα
[00:36.46]cos(π+α)=-cosα
[00:38.66]tan(π+α)= tanα
[00:40.69]sin(π-α)= sinα
[00:42.85]cos(π-α)=-cosα
[00:45.02]tan(π-α)=-tanα
[00:47.22]These are all those"name do not -change"
[00:49.21]As pi goes to half pi the difference shall be huge
[00:51.69]sin(π/2+α)=cosα
[00:53.71]cos(π/2+α)=-sinα
[00:55.76]tan(π/2+α)=-cotα
[00:57.59]
[00:58.11]sin(π/2-α)=cosα
[01:00.00]cos(π/2-α)=sinα
[01:02.14]tan(π/2-α)=cotα
[01:04.04]
[01:08.80]That is to say the odds will change evens are conserved
[01:12.70]The notations that they get depend on where they are
[01:16.97]But no matter where you are
[01:19.36]I've gotta say that
[01:21.47]If you were my sine curve I'd be your cosine curve
[01:25.78]I'll be your derivative you'll be my negative one
[01:30.09]As you change you amplitude I change my phase
[01:33.98]We can oscillate freely in the external space
[01:37.96]
[01:38.54]As we change our period and costant at hand
[01:42.61]We travel from the origin to infinity
[01:46.54]
[01:47.16]It's you sine and you cosine
[01:51.46]Who make charming music around the world
[01:55.55]It's you tangent cotangent
[01:59.76]Who proclaim the true meaning of centrosymmetry
[02:03.62]
[02:47.09]You wanna measure width of a river height of a tower
[02:49.42]You scratch your head which cost you more than an hour
[02:51.45]You don't need to ask any"gods" or" master" for help
[02:53.62]This group of formulas are gonna help you solve
[02:55.75]sin(α+β)=sinα•cosβ+cosα•sinβ
[02:59.00]cos(α+β)=cosα•cosβ-sinα•sinβ
[03:02.32]tan(α+β)=(tanα+tanβ)/(1-tanα•tanβ)
[03:05.49]
[03:06.45]sin(α-β)=sinα•cosβ-cosα•sinβ
[03:09.80]cos(α-β)=cosα•cosβ+sinα•sinβ
[03:12.93]tan(α-β)=(tanα-tanβ)/(1+tanα•tanβ)
[03:18.10]As you come across a right triangle you fell easy to solve
[03:20.41]But an obtuse triangle gonna make you feel confused
[03:22.52]Don't worry about what you do
[03:23.65]There are always means to solve
[03:24.70]As long as you master the sine cosine law
[03:26.68]
[03:30.25]At this moment I've got nothing to say
[03:33.62]
[03:34.14]As trig-functions rain down upon me
[03:37.98]
[03:38.69]At this moment I've got nothing to say
[03:42.65]Let's sing a song about trig-functions
[03:46.68]
[03:47.22]Long live the trigonometric functions
