If sin x° = 0.67, find the value of

(i) cos x°

(ii) cos x° + tan x°

(i) Given,

sin x° = 0.67
sin 42° = .6691       (From tables)
Difference = .0009
Mean difference for 4' = .0009
x° = 42° + 4' = 42° 4'.

Finding cos x°,

cos 42° = .7431
Mean difference of 4' = .0008
cos 42° 4' = .7431 - .0008 = .7423

Hence, the value of cos 42° 4' = .7423

(ii) Calculating tan x°

tan 42° = .9004
Mean difference of 4' = .0021
tan 42° 4' = .9004 + .0021 = .9025

⇒ cos x° + tan x° = .7423 + .9025 = 1.6448

Hence, the value of cos x° + tan x° = 1.6448.