Question

An angle measuring 570 degrees is drawn in standard position. In what quadrant does the terminal side of this angle lie? Express your answer as a Roman numeral.

Answer 1

A whole revolution is equal to 360°. The quadrants in the Cartesian plane is divided as such,
Quadrant I : 0° to 90°
Quadrant II: greater than 90° to 180°
Quadrant III: greater than 180° to 270°
Quadrant IV: greater than 270° to 360°
To answer the question above, we determine the remainder when we divide 570° by 360°.
570° ÷ 360° = 1 remainder 210
Since, the remainder is 210° the terminal side of the angle lies in Quadrant III.