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3 years ago

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">

Mathematics

1 answer:

Yakvenalex [24]3 years ago

7 0

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.

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