Find the value of the following :

(i) tan 15° 2'

(ii) tan 53° 14'

(iii) tan 82° 18'

(iv) tan 6° 9'

(i)

tan 15° 2' = tan(15° 0' + 2')
tan 15° 0' = .2679
Mean difference of 2' = .0006       (To be added)
tan 15° 2' = .2679 + .0006 = .2685

Hence, the value of cos 15° 2' = .2685

(ii)

tan 53° 14' = tan(53° 12' + 2')
tan 53° 12' = 1.3367
Mean difference of 2' = .0016       (To be added)
tan 53° 12' = 1.3367 + .0016 = 1.3383

Hence, the value of cos 53° 12' = 1.3383

(iii)

tan 82° 18' = 7.3962 (directly from tables)

Hence, the value of tan 82° 18' = 7.3962

(iv)

tan 6° 9' = tan (6° 6' + 3')
tan 6° 6' = .1069
Mean difference of 3' = .0009       (To be added)
tan 6° 9' = .1069 + .0009 = .1078

Hence, the value of tan 6° 9' = 0.1078