What quadrant does 24𝜋/5 lie in?

Answer 1

24pi/5 = 25pi/5 - pi/5 = 5pi - pi/5

-pi/5 is in quadrant IV, rotate it 180 degrees (or pi radians). 24pi/5 is in quadrant II.

or another method: 24pi/5 = 24(180)/5 = 24(36) = 864. divide by 360 and look at the remainder: 864/360 has remainder of 864-720 = 144 degrees. 144 degrees is in quadrant II.

Answer 2

Each quadrant contains π/2 radians, so if we go counterclockwise 24π/5 radians we will pass through

(24π/5) / (π/2) quadrants = 48/5 = 9.6 quadrants

As there are 4 quadrants in the circle we go through

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 ...

So after 9 quadrants we get to quadrant 2

So the angle will be in quadrant 2