(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...
Question 1 Report
(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 \(\frac{(3.68)^{2} \times 6.705}{\sqrt{0.3581}}\)
Answer Details
(a)(i) From tables, \(\sin 63.35° = 0.8937\).
\(2\sin 63.35° = 2 \times 0.8937 = \mathbf{1.787}\)
(ii) \(\cos 44.74° = 0.7103\).
\(\log \cos 44.74° = \log 0.7103 = \bar{1}.8515 \;(= -0.1485)\)
(b) \(\log K - \log(K-2) = \log 5\)
\(\log\!\left(\dfrac{K}{K-2}\right) = \log 5 \ \Rightarrow\ \dfrac{K}{K-2} = 5\)
\(K = 5(K-2) = 5K - 10 \ \Rightarrow\ 4K = 10 \ \Rightarrow\ \mathbf{K = 2.5}\)
(c) Evaluate \(\dfrac{(3.68)^2 \times 6.705}{\sqrt{0.3581}}\) using logarithms.
| Expression | Log |
|---|---|
| \((3.68)^2\) | \(2 \times 0.5658 = 1.1316\) |
| \(6.705\) | \(0.8264\) |
| Numerator total | \(1.9580\) |
| \(\sqrt{0.3581}\) | \(\tfrac{1}{2}(\bar{1}.5540) = \bar{1}.7770\) |
\(\text{Log of answer} = 1.9580 - \bar{1}.7770 = 1.9580 + 0.2230 = 2.1810\)
Antilog \(2.1810 = \mathbf{151.7}\) (4 s.f.).
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