A/sina=B/sinb=C/sinc=2R(A B C is the three sides of the angle A B C, and r is the radius of the circumscribed circle of the triangle).

Cosine value:

cosα=(B^2+C^2-A^2)/2BC

cosb=(A^2+C^2-B^2)/2AC

cosc=(A^2+B^2-C^2)/2AB

Sine theorem is a basic theorem in trigonometry, which points out that "in any plane triangle, the ratio of sine value of each side to its diagonal is equal and equal to the diameter of the circumscribed circle", that is, a/sinA=b/sinB=c/sinC= 2r=D(r is the radius of the circumscribed circle and d is the diameter).

Theorem significance:

The sine theorem points out the relationship between the three sides of an arbitrary triangle and the sine value of the corresponding angle. According to the monotonicity of sine function in interval, sine theorem describes a quantitative relationship between the sides and angles of any triangle.

Generally speaking, the three angles A, B and C of a triangle and their opposite sides A, B and C are called elements of a triangle. It is known that the process of finding other elements from several elements of a triangle is called triangle solution. Sine theorem is an important tool to solve triangles.

Refer to the above? Baidu encyclopedia-sine theorem