Way past OP's test date, but on the off chance that anyone having trouble with trig identities stumbled upon this and is having trouble memorizing the graph, I actually find it easier to think of the whole thing like a regular graph - you already know what that looks like, so you can just derive everything from that knowledge.
Quadrant I: You know by looking at the graph that x-values (cos) and y-values (sin) are positive. Therefore, it also follows that tan will be positive as well.
Quadrant II: x (cos) is negative, while y (sin) is positive. Therefore tan will be negative.
Quadrant III: x (cos) and y (sin) are negative. Therefore tan will be positive.
Quadrant IV: x (cos) is positive, while sin is negative. Therefore tan will be negative.