Trig

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19pi/7
Which quadrant does the terminal side lie on?

• Trig -

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

• Trig -

Some students can see this better when visualizing it in degrees
19π/7 radians = 19(180)/7 ° = 488.57..°
= co-terminal with 488.57-360 or 128.57..°

which would be in quadrant II

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