Mathematics
Using tables, find the values of:
(i) cos 48° 36′
(ii) cos 23° 6′
(iii) cos 70° 17′
(iv) cos 85° 8′
Trigonometric Identities
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Answer
(i) Given,
cos 48° 36′
⇒ cos 48° 36′ = cos 48° 36′
From table we have,
cos 48° 36′ = 0.6613
Mean difference of 0′ = 0.0000
Therefore,
cos 48° 36′ = 0.6613
Hence, cos 48° 36′ = 0.6613.
(ii) Given,
cos 23° 6′
⇒ cos 23° 6′ = cos 23° 6′
From table we have,
cos 23° 6′ = 0.9198
Mean difference of 0′ = 0.0000
Therefore,
cos 23° 6′ = 0.9198
Hence, cos 23° 6′ = 0.9198.
(iii) Given,
cos 70° 17′
⇒ cos 70° 18′ − 1′
From table we have,
cos 70° 18′ = 0.3371
Mean difference of 1′ = 0.0003 (to be added)
Therefore,
cos 70° 17′ = 0.3371 + 0.0003
cos 70° 17′ = 0.3374
Hence, cos 70° 17′ = 0.3374.
(iv) Given,
cos 85° 8′
From table we have,
cos 85° 6′ = 0.0854
Mean difference of 2′ = 0.0006 (to be subtracted)
Therefore,
cos 85° 8′ = 0.0854 − 0.0006
cos 85° 8′ = 0.0848
Hence, cos 85° 8′ = 0.0848.
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