(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}})
Explanation
(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 = 2frac{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)