You can use a calculator to find the cosine of 12/13, then just convert to radians.
We know the coordinates point of is (12, 5) using the Pythagorean theorem. Cosine gives us the adjacent side and hypotenuse of the triangle, so we need the opposite side to form an x and y.
For part E you can just use the quadrant rule to find the other trigonometric ratios. For example Q1 is theta, Q2 is pi - theta...and so on.