The essence of trigonometric function is the mapping between any set of angles and a set of ratio variables. The usual trigonometric function is defined in a plane rectangular coordinate system. Its definition field is the whole real number field. 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.

Extended data:

Common sum angle formula

1、sin(α+β)=sinαcosβ+ sinβcosα

2、sin(α-β)=sinαcosβ-sinB*cosα

3、cos(α+β)=cosαcosβ-sinαsinβ

4、cos(α-β)=cosαcosβ+sinαsinβ

5、tan(α+β)=(tanα+tanβ)/( 1-tanαtanβ)