1 radian convert into degree minute second ?

Question

6269 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-14T20:55:02

#57^@ 17' 45#"

The approximation #pi ~~ 355/113# is good enough to calculate this.

Note that #2pi# radians is #360^@#

So #1# radian in degrees is:

#360/(2pi) = 180/pi ~~ (180 * 113)/355 = 20340/355 = 4068/71 = 57 + 21/71#

Then:

#(21 * 60)/71 = 1260/71 = 17 + 53/71#

Then:

#(53 * 60)/71 = 3180/71 = 44 + 56/71 ~~ 45#

So #1# radian is approximately #57^@ 17' 45#"