How do you mark a point on a unit circle given real numbers?

The key fact that will allow you to solve all of these questions is that one "trip" around the circumference of a unit circle is 2*pi radians. The convention is that you always start at the point (1,0) and travel counterclockwise, so that you pass through the quadrants in order from first to fourth. So, for example, part a) is asking where you are on the unit circle if you start at (1,0) and travel 2.4 radians counterclockwise. Well, where are you? You have gone 2.4/(2*pi) = .38197 or about 38% of the way around the circle. You have made it more than one quarter of the way, but less than half of the way around. That puts you in the second quadrant.

Performing the same calculation for the other parts of the question:

b) 7.5/(2*pi) = 1.19366

c) 32/(2*pi) = 5.092958

d) 320/(2*pi) = 50.92958

The only trick for these last three parts is that in all cases you've gone completely around the circle at least once, so you have to discard the full trips around and only look at the fraction of the next trip. For part c) for example, you've gone all the way around five times and gotten .092958 (about 9%) of the way on your sixth trip around. .092958 is greater than 0 but less than a quarter, so you must be in the first quadrant.