The symbol looks at the quadrant. This is the conversion formula between trigonometric functions. In the change, a is regarded as an acute angle,+is counterclockwise rotation,-is clockwise rotation, and the sign depends on the corresponding quadrant after the angle change.

The abscissa is positive and the ordinate is positive as the first quadrant.

The negative abscissa and the positive ordinate are the second quadrant.

Negative abscissa and negative ordinate are the third quadrant.

The positive abscissa and negative ordinate are the fourth quadrant.

When parity remains unchanged, symbols are not considered for the time being:

1. When k is an odd number, the abscissa and ordinate of the point p' (y, x) on the terminal side are just opposite to those of the point P(x, y) on the original terminal side, so the corresponding triangle ratio will change.

2. When k is an even number, the abscissa and ordinate of the point p' (x, y) on the terminal side and the point P'( x, y) on the original terminal side have not changed, so the corresponding triangle ratio remains unchanged.

Symbol sees quadrant: When using this formula, it is assumed that the original angle is an acute angle, because any triangle ratio of the acute angle is positive, so it is not necessary to consider the positive or negative situation of the triangle ratio itself when judging symbols.