geometry and trigonomitry test revision

7/31/2019 Geometry and Trigonomitry Test Revision

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Trigonometry

Question 1 Marks

(a)Find the exact value of

7

cos 12

in simplest surd form, with a rational denominator. 3

(b)A boat ramp is to be made with an angle of 30 and base length 5m.

What is the exact length of the surface of the ramp? 2

(c)Two sides of a triangle are of length 4cm and 9cm respectively. If the area of the

triangle is 9cm2, find the size of the angle between the two given sides. 3

(d)Given that3

sin15

and cos 0 , find the exact value of tan . 2

(e)Find the exact values of:

(i) sin60 1

(ii) tan 60 sec 240 2

(f) Sketch cosy x for 0 360x

. 1


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Question 2 Marks

(a)Simplify sin cot 1

(b)Prove the trigonometric identity:

1cot tan

sin cosx x

x x . 3

(c)Solve the trigonometric equations for 0 360x :

(i)3

cos2

x 2

(ii) sin (sin 1) 0x x 2

(d) (i) Show that sin3tan 2 tan .cos 2 cos

xx x

x x 2

(ii) Hence, or otherwise, solve the equation tan 2 tan 0x x for 0 .2

x

1


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Question 3 Marks

(a) If tan24

7 and sin is positive, find the value ofcos . 3

(b) Find the values of 3600 , , for which2

32 sin 3

(c)

In the diagram above, OD = AB = BC= 50 metres and OA = OB.

(i) Find the size ofAOD , correct to the nearest minute. 2

(ii) Find the size ofAOC, correct to the nearest minute. 2

(d) Simplify4 2 2sin sin cos 2

(e) Determine the exact value of 1 12cos 2sin13

. 3

O

CA D B

50 m

50 m

50 m

Not to scale


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Geometry

Question 1 (12 marks) Use a SEPARATEwriting booklet. Marks

(a)

Find the value of the pronumeral,y, giving reasons for your answer. 3

(b)

ABCD is a rhombus. CB and CD are produced toEand Frespectively

such thatBE = DF.

(i) Show that ADFABE . 3

(ii) Show that AECF is a kite. 2

y

141

68

Not to scale

A B

E

C D

F

A

F E

DB

C

Not to scale


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(c)

In the diagram,RS//PQ and ST//RP.

(i) Prove that the trianglesRSTand QRP are similar. 2

(ii) Find the length ofST, giving reasons for your answer. 2

T

S

R Q

P

3

8 12

2.5

Not to scale

geometry and trigonomitry test revision

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