Answer :

SageRage

Answer:

3rd quadrant

Step-by-step explanation:

  • First we just convert the angle from radians to degrees
  • [tex]\frac{31\pi radians }{6}*\frac{180degrees}{\pi radians} =\frac{31*180}{6} degrees=930degrees[/tex]
  • Now that's too big, all this means is if we start rotating from the positive y-axis in a circle we will cross the starting point 2 times, 2 full circles;
  • [tex]930degrees-360degrees=570degrees\\570degrees-360degrees=210degrees[/tex]  
  • Now in which quadrant it 210 degrees?
  • 0 degrees to 90 degrees is 1st quadrant
  • 90 degrees to 180 degrees is 2nd quadrant
  • 180 degrees to 270 degrees is 3rd quadrant
  • 270 degrees to 360 degrees is 4th quadrant
  • So our answer is the 3rd quadrant.

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