Question

Calculate the angle of (a) 1° (b) 1` (C) 1`` in radians. Use 360°= 2π rad, 1°=60` and 1`=60``

Answer 1

⇒ 360° = 2π rad 

⇒ ° = 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