From Förberedande kurs i matematik 1

The angle \displaystyle -v\text{ } is the reflection of the angle \displaystyle v in the \displaystyle x -axis, and under such reflection the \displaystyle x -coordinate does not change, whereas the \displaystyle y -coordinate changes sign. This means that if \displaystyle \text{sin }v=a, then \displaystyle \text{sin }\left( -v \right)=-a.