Question

Calculate the angle of
(a) 10 (degree) (b) 1′ (minute of arc or arcmin)
and (c) 1″ (second of arc or arc second) in
radians. Use 3600=2π rad, 10=60′ and
1′ = 60 ″

Answer 1

use concept,
   360° = 2π rad 
    1° = 2π/360rad
so, 10° = 10 × 2π/360 rad = π/18 rad

1' ( it means minute ) 
60 minutes (60') = 1° 
1 minute = 1/60° 
but 1° = π/180 rad 
so, 1/60° = π/60×180 = π/10800 rad 

1'' = ? rad 
60'' = 1 minute 
and 60' = 1° so, 3600'' = 1° 
so, 1'' = π/180×3600 = π/648000 rad

Answer 2

Answer:

use concept,

  360° = 2π rad 

   1° = 2π/360rad

so, 10° = 10 × 2π/360 rad = π/18 rad

1' ( it means minute ) 

60 minutes (60') = 1° 

1 minute = 1/60° 

but 1° = π/180 rad 

so, 1/60° = π/60×180 = π/10800 rad 

1'' = ? rad 

60'' = 1 minute 

and 60' = 1° so, 3600'' = 1° 

so, 1'' = π/180×3600 = π/648000 rad

hope this helps