Question

Calculate the angle of (a) 1° ,(b) 1 minute of arc (c) 1 second of arc in radians .

Answer 1

we know, π radian = 180°
Or, 180° = π radian
or, 1° = π/180 radian

(a) Hence, 1° = π/180 radian
(b) 1° = 60' [ here ' indicates minute]
∵ 1 ° = π/180 radian
∴ 60' = π/180 radian
∴ 1' = π/(180 × 60) = π/10800 radian
Hence, 1 min = π/10800 radian
(c) 1' = 60" [ " indicates second]
∵ 1 ' = π/10800 radian
∴ 60" = π/10800 radian
∴ 1" = π/(10800 × 60) = π/648000 radian
Hence , 1" = π/648000 radian

Answer 2

Answer:

we have360°=2πrad

1°={π/180}rad=1.745×10-2rad

b) 1°=60`=1.745×10-2rad

1`=2.908×10-4raf; 2.91×10-4rad

c) 1`=60``=2.908×10-4rad

1``=4.847×10-6rad;4.85×10-6rad