# What quadrant does cot 325^@ lie in and what is the sign?

You can answer which quadrant by referring to a unit circle. Quadrant I runs from ${0}^{o}$ to ${90}^{o}$, quadrant II from ${90}^{o}$ to ${180}^{o}$, quadrant III from ${180}^{o}$ to ${270}^{o}$ and quadrant IV from ${270}^{o}$ to ${360}^{o}$.
The angle given in the problem is ${325}^{o}$ which lies between ${270}^{o}$ and ${360}^{o}$ which puts it in quadrant IV.
As for the sign, cosine is equivalent to the $x$ position and sine is equivalent to the $y$ position. Since quadrant IV is to the right of the $y$-axis, in other words, a positive $x$ value, $\cos \left({325}^{o}\right)$ will be positive.