If θ is acute and cos θ = .7258, find the value of

(i) θ

(ii) 2 tan θ - sin θ

(i) Given,

cos θ = .7258
cos 43° 30' = .7254
Difference = .0004
Mean difference of 2' = .0004
θ = 43° 30' - 2' = 43° 28'.

Hence, the value of θ = 43° 28'.

(ii) Putting, θ = 43° 28' in 2 tan θ - sin θ,

Finding value of tan 43° 28',

tan 43° 24' = .9457
Mean difference of 4' = .0022
tan 43° 28' = .9457 + .0022 = .9479

Finding value of sin 43° 28',

sin 43° 24' = .6871
Mean difference of 4' = .0008
sin 43° 28' = .6871 + .0008 = .6879

2 tan θ - sin θ,

⇒ 2 × .9479 - .6879
⇒ 1.8958 - .6879
⇒ 1.2079

Hence, the value of 2 tan θ - sin θ = 1.2079