Question

Find the value of sin22°14' + cos 75°13'.
(Refer the trigonometric table for the values)

• A. -0.6334
• B. 0.6334
• C. 0.6831
• D. -0.6831

Answer 1

The correct option is B 0.6334

We can write,
22°14' = 22°12' + 2'
From the table we have, sin22°12' = 0.3778
Mean difference for 2′ = 5

sin22°12' = 0.3778
2′ = + 5 (Mean difference to be added for sine)
____________________
sin22°14' = 0.3783 ... (i).

We can write,
75°13' = 75°12' + 1'
From the table we have, cos75°12' = 0.2554
Mean difference for 1′ = 3

cos75°12' = 0.2554
1′ = - 3 (Mean difference to be subtracted for cosine)
____________________
cos75°13' = 0.2551 ... (ii)

From equations (i) and (ii), we get
sin22°14' + cos75°13' = 0.3783 + 0.2551
sin22°14' + cos75°13' = 0.6334