Identity: sec^2(x) = 1 + tan^2(x) => tan^2(x) = sec^2 (x) – 1

sec(x) = √[37/6] => sec^2 (x) = 37/6

tan^2 (x) = 37/6 – 1 = 31/6

tan (x) = +/- √[31/6]

Given that sin (x) is negative and sec (x) is positive, we are in the fourth quadrant, so the tangent is negative, then:

tan (x) = – √[31/6] = – 2.27