Find the value of the following :

(i) sin 35° 22'

(ii) sin 71° 31'

(iii) sin 65° 20'

(iv) sin 23° 56'

(i)

sin 35° 22' = sin (35° 18' + 4')
sin 35° 18' = .5779
Mean difference for 4' = .0010       (To be added)
sin 35° 22' = .5779 + .0010 = .5789

Hence, the value of sin 35° 22' is .5789

(ii)

sin 71° 31' = sin (71° 30' + 1')
sin 71° 30' = .9483
Mean difference for 1' = .0001       (To be added)
sin 71° 31' = .9483 + .0001 = .9484

Hence, the value of sin 71° 31' is .9484

(iii)

sin 65° 20' = sin (65° 18' + 2')
sin 65° 18' = .9085
Mean difference for 2' = .0002       (To be added)
sin 65° 20' = .9085 + .0002 = .9087

Hence, the value of sin 65° 20' is .9087

(iv)

sin 23° 56' = sin (23° 54' + 2')
sin 23° 54' = 0.4051
Mean difference of 2' = .0005       (To be added)
sin 23° 56' = .4051 + .0005 = .4056

Hence, the value of sin 23° 56' is .4056