In which quadrant does −580° lie?

Think it through first, then pick an option.

Answer and explanation

Correct answer: b 2nd

-580° + 2 × 360° = 140°, which lies between 90° to 180°; so the 2nd quadrant.

Why the other options are wrong

a 1st: The 1st quadrant holds angles from 0° to 90°; the equivalent angle of -580° is 140°, so it is not this one.
c 3rd: The 3rd quadrant holds angles from 180° to 270°; the equivalent angle of -580° is 140°, so it is not this one.
d 4th: The 4th quadrant holds angles from 270° to 360°; the equivalent angle of -580° is 140°, so it is not this one.