trigonometric functions - 天儿

词：天儿

曲：天儿

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 do not -change"

As pi goes to half pi the difference shall be huge

sin(π/2+α)=cosα

cos(π/2+α)=-sinα

tan(π/2+α)=-cotα

sin(π/2-α)=cosα

cos(π/2-α)=sinα

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

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 triangle 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