Sin:? In a right triangle, the ratio of the opposite side to the hypotenuse of ∠ α (non-right angle) is called sinα of ∠α, that is, the hook-chord ratio. The "string" in the ancient "hook three strands, four strings and five" is the hypotenuse in the right triangle. The thigh is a human thigh. The ancients called the long right side of a right triangle "thigh".

Application: In a right triangle, ∠ α (non-right angle), the opposite side of sinα=∠α=∠α/the hypotenuse of ∠α.

sin(α+β)=sinα cosβ+cosα sinβ

sin(α-β)=sinα cosβ-cosα sinβ

sin(2a)=2sina*cosa

Extended data theorem

Sine function theorem: in a triangle, the ratio of sine of each side to its diagonal is equal, that is, a/sin A = b/sin B = c/sin C.

Application of sine function theorem in calculating triangle area

S△=c2sinAsinB/2sin(A+B)(S△ is the area of a triangle, with three angles ∠A∠B∠C and opposite sides respectively).

Sdelta =1/2acsinb =1/2bcsina =1/2absinc (three angles ∠A∠B∠C, opposite sides are A, B and C respectively, see trigonometric function).

In addition, when the value of sin is between 180~360, a negative value will appear, and it will appear repeatedly above 360.