# Which quadrant does the given angle 2009 degrees lie?

Oct 18, 2016

$2009$ is located into the third quadrant.

#### Explanation:

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

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

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

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

So $2009$ is located into the third quadrant.