If tanθ = -root 11/5, first draw a right triangle, lable θ. Since tan is opposite/adjacent, root 11 is opposite and 5 is adjacent.
Putting the numbers into Pythagorean theorem to find hypotenuse gives a hypotenuse of 6.
Cos is - (given), and is adj/hyp
Sec is the inverse of Cos which would then be hyp/adj
since hyp was solved to be 6, and adjacent was given to be 5,
Sec θ = -6/5