Ok, so
Let me explain to you:
We have a xy-plane. Remember that cos(x) is a relation in a right triangle which relations the adjacent side of the angle and its hypotenuse.
In this case, we're going to analyze the sign of this relation, like this:
In the first quadrant, we notice that the adjacent side of the angle always takes positive values. And the hypotenuse is always positive, so, if we do a ratio, cos(x) will be positive.
In the second quadrant, we can see that x-axis (adjcent side) takes negative values. And the hypotenuse is always positive, so, if we do the ratio, cos(x) will be negative here.
In the third quadrant, cos(x) is also negative for the same reason.
In the fourth quadrant, cos(x) is positive.
We would conclude that the sign of cos(x) depends of the quadrant, if x-axis is positive, or not.