1004
EXAMINATION EAFERS.
Value.
TRIGONOMETRY AND LOGARITHMS.
Honours Grade.
Thursday, 22nd June.—2 p.m. to 3.30 p.m.
All ordinary symbols and contractions are allowed.
All the steps of the proofs must be given.
Before attempting to answer any question, candidates should read'
the whole of it very carefully, since time is often lost through mis¬
apprehension as to what is really required.
Additional marks will be given for neatness, good style, and
accurately drawn figures.
Candidates may answer six questions only, namely, Nos. 1, 2, 3,.
and one of the alternatives in each of Nos. 4, 5, 6.
1. Explain some method by which the height and distance of an
incessible mountain top can be found, assuming that two places
of observation of known positions and in the same vertical
plane as the summit can be obtained.
If A, B, C, D be four points in a plane, and AB = 8745 feet,
Z. DAB = 36° 10', Z. DBA = 51° 25', z CAD = 58° 40',
Z_ ACD — 84° 17', find CD by the help of the logarithmic
tables.
2. Draw the graphs
(1) y = sin 2x, (2) y = sin a; cos 2a;, from a; = 0 to a; =• tt ;
using the values of sines and cosines given in the tables if you
find it convenient to do so.
From your drawing find an approximate solution to the equation
sin x — tan 2a:.
Verify your solution by solving the equation in the ordinary way so as
find cos x, and then referring to the table of cosines.
3. Find the limits between which x must lie in order that the equation
may give real values of 0.
When this condition is satisfied, find the limits between which these
real values of 6 must lie.