Determine two pairs of polar coordinates for the point (5, -5) with 0° ≤ θ < 360°.

now....  the tangent is -1 when the "y" and "x" are of different signs
now, that happens in the 2nd and 4th quadrant, however, let's take a look at our terminal point, 5 , -5

the "x" is positive, the "y" is negative, that means, is the one on the 4th quadrant    

thus