SOLUTION: The point (0,-1) on the unit circle is rotated 315 degrees counter-clockwise. Determine the coordinates of the new point.

Now we subtract 315°-270° and find that the angle between the slanted
radius and the left side of the x-axis is 45° (indicated by the green
curved line, so we label it 45°:



Now from the point in question we draw a perpendicular up 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 45°, then it is isosceles and the sides of the 45° angle are equal.
The hypotenuse is the radius 1.

We can calculate the two equal sides of that right triangle by
the Pythagorean theorem:



Since we know that a = b we can substitute a for b: 











 

So the vertical and horizontal sides of that right triangle 
are both equal to .



The point is in the 3rd quadrant, so both its coordinates are
negative, so the coordinates of the point is (,).



Edwin