Just guessing from your description:

You have 4 cases. In each case, there is a line of 1 unit long, one end at the origin (0,0) where the angle between the line and the x-axis is 30, 45, 120, and 240 degrees (one per case).

They want to know if you draw lines from the other end to the X and Y axes, where do they cross them?

The original line, the axis, and the projected line form a right triangle with the 1-unit line being the hypotenuse. The definitions of sine and cosine (sine = opposite/hypotenuse, cosine = adjacent/hypotenuse) will let you calculate the answer.

One thing to be careful of, most calculators expect the angles to be in radians, not degrees.