Answer:
tan(x) = -1/6
Step-by-step explanation:
We can use the relation between tan and sec:
[tex]\displaystyle\tan{x}=\pm\sqrt{\sec^2{x}-1}\\\\\tan{x}=-\sqrt{\left(\dfrac{\sqrt{37}}{6}\right)^2-1}\quad\text{negative because sine is negative}\\\\=-\sqrt{\dfrac{37-36}{36}}=\boxed{-\dfrac{1}{6}}[/tex]
The tangent of x is -1/6.
