Question

`the \: angle \: of \: measure \: (31\pi)/(6) \: lies \: in \: which \: quadrant`

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Answer 1

3rd quadrant

Explanation:

• First we just convert the angle from radians to degrees
• 
  `(31\pi radians )/(6)*(180degrees)/(\pi radians) =(31*180)/(6) degrees=930degrees`
• 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;
• 
  `930degrees-360degrees=570degrees\\570degrees-360degrees=210degrees`
• 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.