CAMBERWELL GRAMMAR SCHOOL GENERAL MATHEMATICS A UNIT 1

TRIGONOMETRY, COMPLEX NUMBERS ASSESSMENT TASK j K............ .. 114

Name: ....

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Instructions to candidates

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The task contains 9 worked solution questions. Time allowed is 75 minutes

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This task is worth 58 marks.

All answers for this section are to be done by showing appropriate working and solutions in the spaces provided for each question in the answer booklet. Grapics CAS calculators, scientific calculators and two A4 sheets of notes may be used.

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Ql. Find the exact values of each of the following:

(a) sin 570°

lm

(b)

n coss 3

lm

54-049 + 30°)

Cis C

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(c) tan-h-

Im

Q2. Jack competes in orienteering events. In this event he travels on a bearing of 030°T for 3 km, he then changes direction and travels on a bearing of 150°T for 2 kin. (a) Draw a diagram to represent where Jack travelled in this event. 2m

N

(b) How far is Jack from where he started? Give your answer in simplest surd form. 2m

P- = 3 +- l2 - 2,3.2- c.>J,

°

0 d14

4--7

kM

3m

(c) What bearing, to the nearest degree, should Jack take in order to return to where he started.

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Q3. From a point C, by looking due north, a girt can see a beacon at point B. She can also see a tower at point T, which is 5 km away on a bearing of 056°. The tower at point T is due east of the beacon at B. (a) Fill in the measurements and angles described above on the diagram below. lm

(b) Calculate the length of BT, the distance of the tower from the beacon . Give your answer correct to three decimal places. 2m

(c) If she faces the tower and turns a further 220 clockwise the girl can see a mobile phone mast at point M, which is 9 km away. (i) Fill in the measurements and angles described in part (c) above on the diagram below. 1m

(ii) What is the bearing of the mast at point M from C? lm

"

ear

j

L

a C 7 CL-

-w- ^

IM

0757

(iii) Show...