Answer:
[tex]-\dfrac{5\sqrt{11}}{11}[/tex]
Step-by-step explanation:
Use the relationship between the various trig functions.
[tex]\tan{\theta}=\dfrac{\sin{\theta}}{\cos{\theta}}=\dfrac{\left(-\dfrac{5}{6}\right)}{\left(\dfrac{\sqrt{11}}{6}\right)}=-\dfrac{5}{\sqrt{11}}\\\\=-\dfrac{5}{\sqrt{11}}\cdot\dfrac{\sqrt{11}}{\sqrt{11}}=\boxed{-\dfrac{5\sqrt{11}}{11}}[/tex]
