trigonometry

Geometry and trigonometry
Assignment 4
This assignment covers the material contained
in Chapters 12 to 14.
P
The marks for each question are shown in
brackets at the end of each question.
O
Q
R
1. A 2.0 m long ladder is placed against a perpendicular
pylon with its foot 52 cm from the pylon.
(a) Find how far up the pylon (correct to the nearest
mm) the ladder reaches. (b) If the foot of the
ladder is moved 10 cm towards the pylon how
far does the top of the ladder rise?
(7)
2. Evaluate correct to 4 significant figures:
(a) cos 124 ◦ 13 ′ (b) cot 72.68 ◦ (4)
3. From a point on horizontal ground a surveyor
measures the angle of elevation of a church spire
as 15 ◦ . He moves 30 m nearer to the church and
measures the angle of elevation as 20 ◦ . Calculate
the height of the spire. (9)
4. If secant θ = 2.4613 determine the acute
angle θ (4)
5. Evaluate, correct to 3 significant figures:
3.5 cosec 31 ◦ 17 ′ − cot (−12 ◦ )
3 sec 79 ◦ 41 ′ (5)
6. A man leaves a point walking at 6.5 km/h in
a direction E 20 ◦ N (i.e. a bearing of 70 ◦ ). A
cyclist leaves the same point at the same time
in a direction E 40 ◦ S (i.e. a bearing of 130 ◦ )
travelling at a constant speed. Find the average
speed of the cyclist if the walker and cyclist are
80 km apart after 5 hours. (8)
7. A crank mechanism shown in Fig. A4.1 comprises
arm OP, of length 0.90 m, which rotates
anti-clockwise about the fixed point O, and connecting
rod PQ of length 4.20 m. End Q moves
horizontally in a straight line OR.
Figure A4.1
(a) If ∠POR is initially zero, how far does end
Q travel in 1 4 revolution
(b) If ∠POR is initially 40 ◦ find the angle
between the connecting rod and the horizontal
and the length OQ
(c) Find the distance Q moves (correct to the
nearest cm) when ∠POR changes from 40 ◦
to 140 ◦ (16)
8. Change the following Cartesian co-ordinates
into polar co-ordinates, correct to 2 decimal
places, in both degrees and in radians:
(a) (−2.3, 5.4) (b) (7.6, −9.2) (10)
9. Change the following polar co-ordinates into
Cartesian co-ordinates, correct to 3 decimal
places: (a) (6.5, 132 ◦ ) (b) (3, 3 rad) (6)
10. (a) Convert 2.154 radians into degrees and
minutes.
(b) Change 71 ◦ 17 ′ into radians (4)
11. 140 mm of a belt drive is in contact with a pulley
of diameter 180 mm which is turning at 300
revolutions per minute. Determine (a) the angle
of lap, (b) the angular velocity of the pulley, and
(c) the linear velocity of the belt assuming that
no slipping occurs. (9)
12. Figure A4.2 shows a cross-section through a
circular water container where the shaded area
represents the water in the container. Determine:
(a) the depth, h, (b) the area of the shaded