Generally speaking, in rectangular coordinate system, given the unit circle, for any angle α, the vertex of the angle α coincides with the origin, the starting edge coincides with the non-negative semi-axis of the X axis, and the ending edge intersects with the unit circle at point P(u, v), so the ordinate V of the point P is called the sine function of the angle α, and it is recorded as v=sinα. Usually, we use X to represent the independent variable, that is, X represents the size of the angle and Y represents the function value, so we define the trigonometric function y=sin x at any angle, and its definition domain is all real numbers, with the value range of [- 1, 1].

Extended data:

Correlation formula

1, sum of squares relation

(sinα)^2 +(cosα)^2= 1

2, the relationship between products

Sinα = tanα × cosα (that is, sinα/cosα = tanα)

Cosα = cotα × sinα (that is, cosα/sinα = cotα).

Tanα = sinα × secα (that is, tanα/sinα = secα).

3. Reciprocal relationship

tanα × cotα = 1

sinα × cscα = 1

cosα × secα = 1

4. Business relationship

sinα / cosα = tanα = secα / cscα

5. Sine theorem

Sine law 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).