Question

calculate the angle of (a) 1 degree (b) 1 minute (c) 1 second in radians.use 360 degree=2 pai rad, 1 degree= 60 minute and 1minute=60 second

Answer 1

We know that,

                        360° = 2π radians

Hence, 1° = 2 π/ 360 → (1)

             10° = [2 π/ 360° ] x 10 = π/ 18 radians

60 minutes = 1°

Substituting (1),

              60 minutes = 2 π/ 360

             One minute = 2 π/ (360 x 60)

             One minute = π/ 10800 radians → (2)

One second

60 seconds = 1 minute

Substitute (2),

             60 seconds = π/ 10800 radians

             One second = π/ (10800 x 60) radians

             One second = π/ 648000 radians

Answer 2

We know that,

360° = 2π radians

Hence, 1° = 2 π/ 360 → (1)

10° = [2 π/ 360° ] x 10 = π/ 18 radians

60 minutes = 1°

Substituting (1),

60 minutes = 2 π/ 360

One minute = 2 π/ (360 x 60)

One minute = π/ 10800 radians → (2)

One second

60 seconds = 1 minute

Substitute (2),

60 seconds = π/ 10800 radians

One second = π/ (10800 x 60) radians

One second = π/ 648000 radians