Stupid question since most math placement tests aren't, but is this a multiple choice question? Also, I'm guessing you need to find what that exact angle is? This isn't a surefire way to go about doing the problem, but I would try drawing out the unit circle and draw a line with a slope of 3/4 to get an idea of where the point and estimate of the angle is. In correlation to that, you could try drawing a line with slope of 1 since you should know that arctan(1) is equal to pi/4. Since y = (3/4)x is under y = x, you know the angle is a little less than 45 degrees and multiplying it by 2 should still keep you in the first quadrant. So you know your angle should be between about 70 and 90 after multiplying by 2. I know this probably doesn't answer your question or help you at all, but I thought I'd give it a shot and maybe help you see the problem in a different way so you can solve it.

By the way, I believe arctan(3/4) = 36.87 degrees or something like that. So you should have something like cos(73.??). I would guesstimate it to be around .25.

Edit: Or you can try something like these:

SOLUTION: Evaluate without a calculator: A) sin{ Arctan [(-5/13)]} B)cos{ Arcsin[(-3/4)]} C)Arccos[(-square root of 3/2)] D) tan { Arcsin[(-3/4)]}
I don't think they would make you simplify these types of problems on a placement exam, but I'm not too sure.