Answer
$\sin(-\theta)=-\sin\theta$
Work Step by Step
Reference to the right angled triangle
$ \triangle OAL \equiv \triangle OBL$
$OA=OB$
$AL=-BL$
In the right triangle $\triangle OAL$
$\sin \theta=\frac{AL}{OA} \quad\quad\quad$ eq (1)
In the right triangle $\triangle OBL$
$\sin(-\theta)=\frac{BL}{OB}$
Using the property of equivalency of triangle
$OA=OB$
$AL=-BL$ or $-AL=BL$
$\sin(-\theta)=\frac{BL}{OB}=\frac{-AL}{OB}=-\frac{AL}{OB} \quad\quad\quad$ eq (2)
From equation (1) and equation (2)
$\sin(-\theta)=-\sin\theta$
