Question

D%20%20%5C%3A%20lies%20%5C%3A%20in%20%5C%3A%20which%20%5C%3A%20quadrant" id="TexFormula1" title="the \: angle \: of \: measure \: \frac{31\pi}{6} \: lies \: in \: which \: quadrant" alt="the \: angle \: of \: measure \: \frac{31\pi}{6} \: lies \: in \: which \: quadrant" align="absmiddle" class="latex-formula">
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Answer 1

Answer:

3rd quadrant

Step-by-step explanation:

• First we just convert the angle from radians to degrees
• $\frac{31\pi radians }{6}*\frac{180degrees}{\pi radians} =\frac{31*180}{6} degrees=930degrees$
• 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.