2. Cosine function cos(A)=b/c

3. tangent function tan(A)=a/b

4. cotangent function cot (a) = b/a.

Where a is the opposite side, b is the edge and c is the hypotenuse. The usual trigonometric function is defined in a plane rectangular coordinate system.

The domain of trigonometric function is the whole real number domain. The other is defined in a right triangle, but it is incomplete. Modern mathematics describes them as the limit of infinite sequence and the solution of differential equation, and extends their definitions to complex system.

Introduction to the formula of sum and difference of two angles

1、sin(α+β)=sinαcosβ+cosαsinβ

2、cos(α+β)=cosαcosβ-sinαsinβ

3、tan(α+β)=(tanα+tanβ)/( 1-tanαtanβ)

4、sin(α-β)=sinαcosβ-cosαsinβ

5、cos(α+β)=cosαcosβ+sinαsinβ

6、tan(α+β)=(tanα-tanβ)/( 1+tanαtanβ)

General formula of trigonometric function

(1) sin2alpha = 2sinα cosα = 2sinα cosα/(cos2 (α)+sin2 (α)) (because cos 2 (α)+sin 2 (α) = 1).

(2) Divide COS 2 (α) up and down to get SIN 2 α = 2 tan α/( 1+tan 2 (α)).

(3) Replace α with α/2.

supplement

( 1)cos(a+b)= cosa cosb-Sina sinb，cos(a-b)= cosa cosb+Sina sinb； Add the two formulas to get: cos (a+b)+cos (a-b) = 2cosacosb; get cosa cosb =(cos(a+b)+cos(a-b))/2。

(2) Sinasinb =-(cos (a+b)-cos (a-b))/2 is obtained by subtracting two expressions.