You can see α and π+α. .

Let the circle O be a unit circle, then OP=OQ= 1 (in fact, it doesn't matter whether it is a unit circle here).

Sinα= ordinate /OP=b/ 1=b

Sin(π+α)= ordinate /OQ=-b/ 1=-b

So sin (π+α) =-sin α?

(Drawing is mainly to make clear that the trigonometric function in senior high school is arbitrary, and the value of trigonometric function is calculated based on the abscissa and ordinate (scalar), so it may be negative, but for the hypotenuse in junior high school, that is, the OP here? OQ, etc? Always positive by default)

Other trigonometric function inductive formulas can also be proved by drawing or inductive formulas.

In addition, the respondent's "knowing smile" method is also possible, just for the convenience of memorizing symbols.