(a) Using mathematical tables, find ; (i) \(2 \sin 63.35°\) ; (ii) \(\log \cos 44.74°\);
(b) Find the value of K given that \(\log K - \log (K - 2) = \log 5\);
(c) Use logarithm tables to evaluate \(\frac{(3.68)^{2} \times 6.705}{\sqrt{0.3581}}\)
(a)(i) \(\sin 63.35° = 0.8938\)
\(2 \sin 63.35° = 2 \times 0.8938 = 1.7876\)
(ii) \(\log \cos 44.74° = \bar{1}.8514\)
(b) \(\log K - \log (K - 2) = \log 5\)
\(\log (\frac{K}{K - 2}) = \log 5\)
\(\therefore \frac{K}{K - 2} = 5 \implies K = 5(K - 2)\)
\(K = 5K - 10 \implies 10 = 5K - K = 4K\)
\(K = 2\frac{1}{2}\)
(c) \(\frac{(3.68)^{2} \times 6.705}{\sqrt{0.3581}}\)
| No | Log |
| \((3.68)^{2}\) | \(0.5658 \times 2 = 1.316\) |
| \(6.705\) | \(0.8264 = 0.8264\) |
|
= \(1.9580\) |
|
| \(\sqrt{0.3581}\) | \(\bar{1}.5540 \div 2 = \bar{1}.7770\) |
| \(151.7\) | \(\gets 2.1810\) |
\(\therefore \frac{(3.68)^{2} \times 6.705}{\sqrt{0.3581}} = 151.7\)
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