Mathematics
Use tables to find the acute angle θ, if the value of cos θ is :
(i) 0.9848
(ii) 0.9574
(iii) 0.6885
Answer
(i) Let cos θ = 0.9848
From graph,
cos 10° = 0.9848
θ = 10°.
Hence, θ = 10°.
(ii) Let cos θ = 0.9574
From graph,
cos 16° 48' = 0.9573
cos θ - cos 16° 48' = 0.9574 - 0.9573 = 0.0004
From table,
Difference of 1' = 0.0004 [To subtract]
∴ θ = 16° 48' - 1' = 16° 47'.
Hence, θ = 16° 47'.
(iii) Let cos θ = 0.6885
From graph,
cos 46° 30' = 0.6884
cos θ - cos 46° 30' = 0.6885 - 0.6884 = 0.0001
From table,
Difference of 1' = 0.0002 [To subtract]
∴ θ = 46° 30' - 1' = 46° 29'.
Hence, θ = 46° 29' or 46° 30'.
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