I assume you're familiar with the following basic formulas of trigonometry:

cos²x + sin²x = 1

tan x = sin x / cos x

So, if you know that sin (A) = -1/2, you get

cos²A + (-1/2)² = 1 <=> cos²A = 1 - 1/4 <=> cos²A = 3/4

cos A = ± sqrt(3)/2

Whether cos A is positive or negative depends on the quadrant that the angle A is in.

Once you know that sin A = -1/2 and cos A = ± sqrt(3)/2 , you can calculate tan A by applying the second formula:

tan A = (-1/2)/(± sqrt(3)/2) so tan A = ±(1/sqrt(3)) , again depending on the quadrant.

This is my first post on these forums, but I hope I was able to help.