How do you determine the quadrant in which #6.02# radians lies?
I tried this:
Radians are a bit difficult and confusing because it is not easy to "see" the angle as in degrees.
We know that an angle of
When I have an angle in radians and I want to place it in terms of quadrants I always try to evaluate mentally the position by referring to
You can build a mental map of radians for each quadrant:
1st quadrant: from
2nd quadrant: from
3rd quadrant: from
4th quadrant: from
The real trick, anyway, is experience and to use radians extensively to try to get used to them.
You can convert it to degrees, since it then becomes easier to figure it out.
To convert something from radians to degrees, you have to multiply it by a conversion factor of
The logic behind this is that since
And you may know, that multiplying anything by
Also, more importantly, multiplying a
For this particular question, we have been given
Using the conversion factor mentioned above,
#6.02cancel("radians") xx 180^@ / (3.14 cancel("radians")#
#=6.02xx180^@/3.14 = 345.06^@#
Now, to locate
(Although you can guess that it will be in the 4th quadrant because it is slightly less than
In this image, we can see that
Hope this helps :)
We know that their are
My preferred approach is to just learn (or calculate) the quadrants, based on the
If we have an angle,
Then we use the quadrant and trace map out multiples of
So if we take the angle