She's right about the x and y coordinates being respectively 
the cosine and sine of the angle.  But she gave you the wrong 
signed y-coordinate, because she didn't draw the graph.  Mathematics
is all about graphs.  One should always draw graphs, especially
in trigonometry problems.

Below is the graph of what you should draw first.  Since -300° is a 
negative angle, it is formed by a CLOCKWISE rotation of 300 
degrees from the right side of the x-axis.  That rotation is 
indicated by the red arc drawn CLOCKWISE from the right side
of the x-axis to the terminal side. 

So it ends up in the first quadrant, not the fourth, like the other
tutor thought. The coordinates of the point of 
intersection is 



but you have to simplify it.  Here's how:



To simplify the coordinates, draw a radius to the point, and
a vertical line up to the point forming a reference right triangle.
Since the red arc is 300°, and a complete revolution is 360°, the
angle inside the reference right triangle is 360°-300°=60°. The
radius is its hypotenuse. That makes the reference triangle a 
30-60-90 right triangle.   



So the correct coordinate for the point is .

Edwin