If tan(x) = 1/2, what is sec(x) ?

Decide what quadrants this can be in.  Decide if sec can be pos or neg or either.

NOW

Draw a tight angled triangle.

Label one of the acute angles x

now      $$tan x = \frac{1}{2}=\frac{opp}{adj}$$

label the opp side as 1   and the adj side as 2,   work out the 3rdside using the Pythagorean theorem.

$$sec(x)=\frac{1}{cos(x)}=\frac{hyp}{adj}$$         now just take the values from your triangle.    :))