Trig
posted by Jenn .
19pi/7
Which quadrant does the terminal side lie on?

19 pi / 7 =
( 14 + 5 ) * pi / 7 =
( 14 / 7 ) pi + ( 5 / 7 ) pi =
2 pi + ( 5 / 7 ) pi
2 pi + theta = theta
I quadrant 0 ÷ pi / 2
II quadrant pi / 2 ÷ pi
III quadrant pi ÷ ( 3 / 2 ) pi
IV quadrant ( 3 / 2 ) pi ÷ 2 pi
theta = ( 5 / 7 ) pi
theta = 0.7142857 pi
thheta > pi /2
theta < pi
II quadrant 
Some students can see this better when visualizing it in degrees
19π/7 radians = 19(180)/7 ° = 488.57..°
= coterminal with 488.57360 or 128.57..°
which would be in quadrant II