Mathematics

Use tables to find cosine of :

(i) 2° 4'

(ii) 8° 12'

(iii) 26° 32'

(iv) 65° 41'

(v) 9° 23' + 15° 54'

Trigonometric Identities

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Answer

(i) From table,

cos 2° 6' = 0.9993

Difference of 2' = 0       [To add]

∴ cos 2° 4' = 0.9993 + 0 = 0.9993

Hence, 2° 4' = 0.9993

(ii) From table,

cos 8° 12' = 0.9898

Hence, 8° 12' = 0.9898

(iii) From table,

cos 26° 30' = 0.8949

Difference of 2' = 0.0003       [To subtract]

∴ cos 26° 32' = 0.8949 - 0.0003 = 0.8946

Hence, 26° 32' = 0.8946

(iv) From table,

cos 65° 42' = 0.4115

Difference of 1' = 0.0003       [To add]

∴ cos 65° 41' = 0.4115 + 0.0003 = 0.4118

Hence, 65° 41' = 0.4118

(v) Adding,

9° 23' + 15° 54' = 24° 77' = 25° 17'

(As, 60' = 1°)

From table,

cos 25° 18' = 0.9041

Difference of 1' = 0.0001       [To add]

∴ cos 25° 18' = 0.9041 + 0.0001 = 0.9042

Hence, 25° 18' = 0.9042

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