THE HONGKONG GOVERNMENT GAZETTE, 15TH FEBRUARY, 1896.
Class IV.
The Dispute on the Shadow of the Ass.
148
A traveller once journeyed, riding on a hired ass, along a road exposed to the full heat of a burn- ing sun. Not finding so much as a bush under which to take shelter, the thought struck him that it would not be a bad plan to dismount and seat himself in the shadow of the ass.
The owner of the
donkey, who had accompanied him, objected to this arrangement, declaring that when he hired out the animal to him the shadow was not included in the bargain. A fierce dispute arose between the owner of the ass and its rider, and at last from words they came to blows which finally resulted in an action at law.
It is a mistake to dispute about trifles. Quarrels about little things may lead to serious conse-
quences.
Class V.
The Arab and the Camel,
Once a camel came to the door of a tent and thrust in his nose.
Not being resisted he thrust in his feet. There being no hindrance he came half way in. After a while he got all the way in. Then the Arab said to the camel-" This tent is too small for two." Said the camel to the Arab- "If so, you had better leave."
TRIGONOMETRY.
.1. Shew that the sum of the numbers of degrees and grades contained in any angle is equal to 19
times their difference.
2. Explain the meaning of sin4; and prove that sin {(2n−1) π + A}
*
-sin A.
3. While sailing west I observe two lights north of me: after sailing two miles their bearings are
60° and 30°, respectively, with my course. How far are they apart?
4. Prove geometrically, or otherwise, that
(a) cos (A--B)
cos A cos B + sin A sin B.
tan A+ tan B
(B) tan (A+B)
1
tan A tan B
A + B A B
(y) sin A + sin B
2 sin
COS
2
2
5. Find expressions for the sine and cosine of 34 in terms of the sines and cosines of A.
6. Determine cos 4 in terms of sin4, when A lies between 270° and 450°.
2
7. Prove that-
(a) cos 4A 8 cos1 A
-
8 cos2 A+ 1.
cot A (1 + tan3 2A).
(B) (cot 4+ tan 24)*
(y) sin (y-ẞ) sin (8-a) + sin (a-y) sin (8-8) + sin (B-a) sin (8-y) = 0.
8. Solve, giving the solution in general terms,-
9. Explain what is meant by 4
1
sin a+ cos x ✓ 2.
=
sina.
and prove that sin−1 + cot-1 3
√5
10. In any triangle prove that--
(a) sin A + sin B + sin C 4 cos + cos
(b) sin A: sin B: sin C:: a:b: c.
11. Express the cosine of an angle of a triangle in terms of the sides.
C
cos -.
Find the radius of the circle inscribed in a triangle in terins of the sides and area of the triangle.
12. Show how to solve a triangle, having given-two sides and the included angle.
=
Find A and B when a 21, b = 11, 34° 42′ 30"; having given log 23010300, L tan
72° 38′ 45′′
10.5051500.