# How do you determine the quadrant in which 3.5 radians lies?

$3.5$ radians lies in quadrant III.
Since we know the measure in degrees of multiples of $\frac{\pi}{2}$ radians, it would be nice to create an inequality that contains $3.5$ radians. We will use the approximation $\pi \approx 3.14$ and from that it follows that $\frac{\pi}{2} \approx 1.57$. Since $3.14 < 3.5 < 3.14 + 1.57$, we can write this inequality like this: $\pi < 3.5 < \frac{3 \pi}{2}$. Since we know that $\pi$ radians is equal to ${180}^{o}$ and $\frac{3 \pi}{2}$ radians is equal to ${270}^{o}$, 3.5 radians lies in the third quadrant.