Q.The value of $\sin(-420^\circ)$ is :

For an angle $\theta$ in standard position with a point $P(x,y)$ on its terminal side at distance $r=\sqrt{x^2+y^2}$ from the origin, the six trigonometric ratios are $\sin\theta=y/r$, $\cos\theta=x/r$, $\tan\theta=y/x$, $\operatorname{cosec}\theta=r/y$, $\sec\theta=r/x$, $\cot\theta=x/y$. Since $r>0$ always, the sign of a ratio depends only on the signs of $x$ and $y$, i.e. on the quadrant. The All–Sin–Tan–Cos rule summarises which ratios are positive in quadrants I, II, III, I …