Answer
$-\frac{2\sqrt {10}}{3}$
Work Step by Step
1. Let $cos^{-1}(-\frac{3}{7})=t$ (quadrant II), we have $cos(t)=-\frac{3}{7}$
2. Let $x=-3, r=7$, we have $y=\sqrt {r^2-x^2}=\sqrt {49-9}=2\sqrt {10}$
3. Thus we have $tan(t)=\frac{y}{x}=-\frac{2\sqrt {10}}{3}$
