The problem states,
If sec(theta) = 3 with theta in QIV find cos(theta), sin(theta) and tan(theta).
you should know that secant is the reciprocal of cosine , so the fact that
$\displaystyle \cos{\theta} = \frac{1}{3}$ should be immediate.
since $\displaystyle \theta$ is in quad IV , you should also know that $\displaystyle \sin{\theta}$ and $\displaystyle \tan{theta}$ are both negative values.
there are two ways to determine the values of sine and tangent ...
1) use of reference triangles
sketch a reference right triangle in quad IV ... since $\displaystyle \cos{\theta} = \frac{1}{3}$, then the adjacent side = 1 and the hypotenuse = 3
the size of the opposite side = $\displaystyle \sqrt{3^2 - 1^2} = \sqrt{8} = 2\sqrt{2}$
since the opposite side has a downward direction, its value is $\displaystyle -2\sqrt{2}$.
$\displaystyle \sin{\theta} = \frac{opp}{hyp} = -\frac{2\sqrt{2}}{3}$
$\displaystyle \tan{\theta} = \frac{opp}{adj} = -\frac{2\sqrt{2}}{1} = -2\sqrt{2}$
2) use of Pythagorean identities ...
$\displaystyle \sin{\theta} = \pm \sqrt{1 - \cos^2{\theta}}$
$\displaystyle \tan{\theta} = \pm \sqrt{\sec^2{\theta} - 1}$
and, of course, you have to determine the correct sign from the quadrant info.