1) Please Show Me How To Convert (-3)radian to Degree-Minutes-Second ?

1 Answer
Apr 27, 2018

#-171° 53'13.2#''

Explanation:

I'm assuming that for degrees and minutes you want integer values.
In general #pi# radians are #180# degrees.
so #-3# radians are #-3*180/pi# degrees or #-171.887339°#

-171 is the closest integer so you have that many degrees.
But, you can't forget about the numbers after the decimal

There are 60 minutes of arc per degree, so
# .887339°*60# = #53.24034# minutes of arc.
Again, we take the closest integer lower than our number, so #53# minutes. This is written as #-171°53'# and read as negative (or minus) 171 degrees, 53 minutes.

Just like in time, there are 60 seconds in a minute.
We have #0.24034# minutes we don't have in our incomplete answer, so we again multiply by #60#.
#60*0.24034# = #13.2# seconds of arc.
We write the complete answer as #-171° 53'13.2#'' and is read as negative (or minus) 171 degrees 53 minutes 13.2 seconds (saying of arc is optional)