No. 26.
735
TRIGONOMETRY.
Note:--Use T-3.1416.
1. The earth being supposed a sphere of which the diameter is 7982 miles, find the length of 4° of the meridian.
Find the answer to 3 places of decimals.
2. Let M N P be a triangle. Draw from N a perpendicular N R on MP and let it be within the triangle.
Write the following ratios :-
Sin N MR, cos N M R, Sin M NR, cot M N R,
tan N MR. cosec M N R.
tan NPR.
Sin N P R, sin P N R,
3. Trace the changes in the sign and magnitude of the secant and cotangent of an angle as the angle increases from 0° to 360°.
4. If a=0°, ẞ-30°, y=45°, 8=60° and 0=90°
find the value of :--
(a) cos a. sin y. cos &
Ө
(b) (Sin 0.
'—cos @ + coséc ẞ) (cos + sec + cot 8).
5. The length of a kite string is 250 yards and the angle of elevation of the kite is 30°, find the height of the kite.
6. Prove the following relation
sin 33+ sin 3°
-
cos 33° + cos 30=tan 18°.
No. 27.
UPPER SCHOOL.
TRANSLATION.
ENGLISH INTO CHINESE.
1. It is reported that Prince Ching and the members of the Grand Council have held several conferences regarding the meeting of Russian and Japanese peace plenipotentiaries at Washington and the question of the future of Manchuria. The Government has also telegraphed to the different Viceroy s and Governors inquiring what attitude China should adopt in the present circumstances.
2. Mahomet's household was of the frugalest; his common diet bread and water; sometimes for months there was not a fire once lighted on his hearth. They record with just pride that he would mend his own shoes and patch his own cloak. A poor, hard-toiling, ill-provided man; careless of what vulgar men toil for. Not a bad man, I should say; something better in him than hunger of any sort, or these wild Arab men, fighting and jostling three and twenty years at his hand, in close contact with him always, would not have reverenced him so!
3. All effectual advancement towards the true felicity of the human race must be by individual, not public effort. Certain general measures may aid, certain revised laws guide, such advancement; but the measure and law which have first to be determined are those of each man's home.
Note.-Boys in Class III may translate one only of the above pieces if they choose.