I would say if sec(x) = sqrt(14)/2 then cos(x) = 2/sqrt(14)

The Six Trigonometric Functions

From here you can use sin^2(x)+cos^2(x) = 1

Subbing in for cos(x) and solving for sin(x) you will get

sin(x) = sqrt(8)/sqrt(14)

Now use tan(x) = sin(x)/cos(x)

This should give tan(x) = sqrt(2), thisanswer is in the 1st quadrant.

tan is negative in the 2nd quadrant so tan(x) = -sqrt(2)