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


    II quadrant

  • 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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