Which quadrant does the given angle 2009 degrees lie?

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Which quadrant does the given angle 2009 degrees lie?

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Answer 1 · 2016-10-18T16:06:11

$2009$ $2009$ is located into the third quadrant.

Explanation:

The first thing is to calculate how many whole turns this angle covers

Dividing $\frac{2009}{360} = 5.58056$ $2009/360=5.58056$ we know that $5$ $5$ whole turns so

$2009 - 5 \cdot 360 = 209 = a$ $2009-5*360=209 = a$ and now

If $0 < a \leq 90$ $0 < a le 90$ first quadrant
If $90 < a \leq 180$ $90 < a le 180$ second quadrant
If $180 < a \leq 270$ $180 < a le 270$ third quadrant
If $270 < a \leq 360$ $270 < a le 360$ fourth quadrant.

So $2009$ $2009$ is located into the third quadrant.

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Which quadrant does the given angle 2009 degrees lie?

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