Mathematics
Using tables, find the values of :
(i) tan 24° 24′
(ii) tan 9° 38′
(iii) tan 31° 27′
(iv) tan 65° 50′
Trigonometric Identities
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Answer
(i) Given,
tan 24° 24′
⇒ tan 24° 24′
From table we have,
tan 24° 24′ = 0.4536
Mean difference of 0′ = 0.0000
Therefore,
tan 24° 24′ = 0.4536
Hence, tan 24° 24′ = 0.4536.
(ii) Given,
tan 9° 38′
⇒ tan 9° 36′ + 2'
From table we have,
tan 9° 36′ = 0.1691
Mean difference of 2′ = 0.0006 (to be added)
Therefore,
tan 9° 38′ = 0.1691 + 0.0006 = 0.1697
Hence, tan 9° 38′ = 0.1697.
(iii) Given,
tan 31° 27′
⇒ tan 31° 24′ + 3'
From table we have,
tan 31° 24′ = 0.6104
Mean difference of 3′ = 0.0012 (to be added)
Therefore,
tan 31° 27′ = 0.6104 + 0.0012 = 0.6116
Hence, tan 31° 27′ = 0.6116.
(iv) Given,
tan 65° 50′
⇒ tan 65° 48′ + 2'
From table we have,
tan 65° 48′ = 2.2251
Mean difference of 2′ = 0.0034 (to be added)
Therefore,
tan 65° 50′ = 2.2251 + 0.0034 = 2.2285
Hence, tan 65° 50′ = 2.2285.
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