# Which quadrant does the terminal side of 530 degrees lie?

Q2

#### Explanation:

When we go all the way around, from positive x-axis to positive x-axis, we go around ${360}^{o}$, and so we can subtract 360 from 530:

${530}^{o} - {360}^{o} = {170}^{o}$

When we move one quarter of the way around, from the positive x-axis to the positive y-axis, we move ${90}^{o}$. So since we've moved more than ${90}^{o}$, we move from Q1 to Q2.

When we move half-way around, from the positive x-axis to the negative x-axis, we move ${180}^{o}$. Since we haven't moved this much, we don't move from Q2 to Q3.

Therefore, we're in Q2.

Another way to do this is to take the rotation and divide it by ${360}^{o}$ - the remainder will tell you which quadrant we end up in. So in our case, we have:

$\frac{530}{360} \cong \textcolor{b l u e}{1} . \textcolor{red}{47}$

which means that we've gone around once (1) and not quite half again (0.47) - which puts us in Q2.