I do not know how to find the angle of the function sec 4x = 2 on the unit cirlce.

I know I would be looking for 2 but I don't know where since it is sec.

sec A = 2

1/cos A = 2
cos A = 1/2
A = 60 degrees or pi/3 radians (also pi - pi/3)
4 x = A
so x = 15 degrees or pi/12 radians

look at the other quadrants and angles A greater than 2 pi because A/4 may be less than 2 pi