SOLUTION: A circle centered at the origin has a radius of 10.If the point(10,0)is rotated 120 degrees counter-clockwise, determine the coordinates of the new point in exact radical form.

Now we subtract 180°-120° and find that the angle between the slanted
line and the left side of the x-axis is 60° (indicated by the green
curved line, so we label it 60°:



Now from the point in question we draw a perpendicular down to the
x-axis:



This forms a special right triangle.  

We are supposed to know that if a right triangle has an acute angle 
of 60°, then one of the sides of the 60° angle is one-half the other.
So since the hypotenuse is 10, its bottom leg is 5.

That tells us that the x-coordinate of the point in question is .





We can calculate the vertical side of that right triangle by
the Pythagorean theorem:















 



So the coordinates of the point is (,).

Edwin