sin(-α)=-sinα，cos(-α)=cosα，sin(π/2-α)=cosα，cos(π/2-α)=sinα，sin(π/2+α)=cosα，cos(π/2+α)=-sinα，sin(π-α)=sinα.

cos(π-α)=-cosα，sin(π+α)=-sinα，tanα=sinα/cosα，tan(π/2+α)=-cotα，tan(π/2-α)=cotα，tan(π-α)=-tanα，tan(π+α)=tanα.

trigonometric function

Trigonometric function is a transcendental function in elementary functions in mathematics. Their essence 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.

The formulas of trigonometric functions seem to be many and complicated, but as long as we master the essence and internal laws of trigonometric functions, we will find that there is a strong connection between the formulas of trigonometric functions. And mastering the inherent law and essence of trigonometric function is also the key to learn trigonometric function well.