Using tables, find the values of:

(i) sin 83° 12′

(ii) sin 61° 14′

(iii) sin 9° 55′

(iv) sin 32° 40′

(i) Given,

sin 83° 12′

⇒ sin 83° 12′

From table we have,

∴ sin 83° 12′ = 0.9930

Mean difference of 0′ = 0.0000

Hence, sin 83° 12′ = 0.9930.

(ii) Given,

sin 61° 12′

⇒ sin 61° 12′ + 1'

From table we have,

sin 61° 12′ = 0.8763

Mean difference of 2' = .0003 (To be added)

sin 61° 14′ = 0.8763 + 0.0003 = 0.8766

Hence, sin 61° 14′ = 0.8766.

(iii) Given,

sin 9° 55′

⇒ sin 9° 54′ + 1'

From table we have,

sin 9° 54′ = 0.1719

Mean difference of 1' = .0003 (To be added)

sin 9° 55′ = 0.1719 + 0.0003 = 0.1722

Hence, sin 9° 55′ = 0.1722.

(iv) Given,

sin 32° 40′

⇒ sin 32° 36′ + 4'

From table we have,

sin 32° 36′ = 0.5388

Mean difference of 4' = .0010 (To be added)

sin 32° 40′ = 0.5388 + 0.0010 = 0.5398

Hence, sin 32° 40′ = 0.5398.