Question

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

Answer 1

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(325^o)` will be positive.