Question

The value of cos69°45' - cos15°40' is .

• A. $-$ 0.6168
• B. 0.6168
• C. $-$ 0.6618
• D. 0.6618

Answer 1

The correct option is A $-$ 0.6168

We can write,
69°45' = 69°42' + 3'
From the table we have, cos69°42' = 0.3469
Mean difference for 3′ = 8 (Mean difference to be subtracted for cosine)
cos69°42' = 0.3469
3′ = - 8
____________________
cos69°45' = 0.3461 ... (i)


We can write,
15°40' = 15°36' + 4'
From the table we have, cos15°36' = 0.9632
Mean difference for 4′ = 3 (Mean difference to be subtracted for cosine)
cos15°36' = 0.9632
4′ = - 3
____________________
cos15°40' = 0.9629 ... (ii)

From equations (i) and (ii), we get
cos69°45' - cos15°40' = 0.3461 - 0.9629 = - 0.6168