Question

How do you determine the quadrant in which `-4.25` radians lies?

Answer 1

Consider multiples of `pi` written in decimal form.

Explanation:

`-4.25` is between `-pi`, which is roughly -3.14, and `-(3pi)/2`, which is roughly -4.71. Each quadrant has a turn of `(3pi)/2` so this means we're looking at a value which is in the third quadrant away from zero. We're counting in the clockwise direction as it's negative, so that takes us to the second (i.e. top left) quadrant.