Question

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

Answer 1

`3.5` radians lies in quadrant III.

Explanation:

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