# Which quadrant does the given angle 621 degrees lie?

Nov 11, 2016

${Q}_{3}$

#### Explanation:

If I remember correctly, this was my way of finding the Q of any

${\theta}^{o}$:

Let q = int ( $\frac{\theta}{90}$ ) be the quotient from the division

$\frac{\theta}{90}$.

If q is even and a multiple of 4, $\theta \in {Q}_{1}$;

otherwise $\theta \in {Q}_{3}$.

If q is odd and the remainder in ( q/4 ) is 1, $\theta \in {Q}_{2}$;

otherwise $\theta \in {Q}_{4}$.

Here, int ( 621/90 ) = 6 that is even but not a multiple of 4.

So, ${621}^{o} \in {Q}_{3}$.

For that matter, int ( 711/90 )= 7 that is odd but not a multiple of 3. So,

${711}^{o} \in {Q}_{4}$,

Int ( 801/80 )= 8 that is even but a multiple of 4. So, ${801}^{o} \in {Q}_{1}$

Int (891/80)= 9 that is odd but a multiple of 3. So, ${891}^{o} \in {Q}_{2}$

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