trigonometric functions歌詞

作詞 : 天兒
作曲 : 天兒
when you first study math about 1234
first study equation about xyzt
It will help you to think in a logical way
When you sing sine, cosine, cosine, tangent
Sine, cosine, tangent, cotangent
Sine, cosine, ..., secant, cosecant
Let's sing a song about trig-functions
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"
As pi goes to half pi the difference shall be huge
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
But no matter where you are
I've gotta say that
If you were my sine curve, I'd be your cosine curve
I'll be your derivative, you'll be my negative one
As you change you amplitude, I change my phase
We can oscillate freely in the external space
As we change our period and costant at hand
We travel from the origin to infinity
It's you sine, and you cosine
Who make charming music around the world
It's you tangent, cotangent
Who proclaim the true meaning of centrosymmetry
B BOX
You wanna measure width of a river, height of a tower
You scratch your head which cost you more than an hour
You don't need to ask any "gods" or" master" for help
This group of formulas are gonna help you solve
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 solve
But an obtuse triange gonna make you feel confused
Don't worry about what you do
There are always means to solve
As long as you master the sine cosine law
At this moment I've got nothing to say
As trig-functions rain down upon me
At this moment I've got nothing to say
Let's sing a song about trig-functions
Long live the trigonometric functions