I got the following question marked wrong and I was wondering if someone could tell me why I got it wrong. The question is of the 6 trigonometric ratios, if only cosine and secant are positive, the angle is in which quadrant? I said it was in the 4th quadrant.

well, cos is 1/sec so if one is + the other is +

In quadrant 4 in fact the cos is +
and also in quadrant 1 the cos is +
but in quad one they are all plus.
It can not be quad 2 or quad 3 because cos is - there.
So I think you are correct.