mathematics-trigonometry1.pdf

8/18/2019 Mathematics-Trigonometry1.pdf

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TRIGONOMETRY

1) Write down the ratios of tan , sin and cos .

5

4

2) Find the exact value of sin , cosec , sec and cot .

7

12

3) If tan 6

11, find the exact ratios of sin and cos .

4) Find the value of x if sin cos39 x .

5) Simplifycot

tan

62

28

.

6) Evaluate if

sec cos 40 2 10

ec

7) Evaluate tan '56 23 correct to 3 decimal places.

8) Find in degrees and minutes if cos . 0 235.

9) Find the value of p in the diagram below, correct to one decimal place.

8

p

43051’


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10) Evaluate x to one decimal place.

7 x

49019’

11) Find in degrees and minutes, to the nearest minute.

2.2

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12) The angle of elevation from Amanda to the top of a tree is 51 34 ' . If Amanda is

standing 5 metres out from the base of the tree, how tall is the tree, to one decimal place?

13) A plane leaves Sydney and flies on a bearing of 235 for 500 km. How far west of

Sydney is the plane, to the nearest km?

14) A bird is perched on top of a 10 m tower, watching a worm down on the ground.

If the angle of depression down to the worm is 67 20 ' , how far does the bird need to fly

down to catch the worm? Answer to one decimal place.

15) Lee starts a bush walk at Katoomba by walking 4 km due north. She then turns

and walks due west for 5 km. Find, to the nearest degree,

(a) Lee’s bearing from Katoomba

(b) the bearing of Katoomba from Lee.

16) Find the exact value of cos 300.

17) Find the exact value of tan 600.

18) Find the exact value of sin 450.

19) Find the exact value of cos 3150.

20) Find the exact value of sin 2400.

21) Find the exact value of tan (-2100)

22) In which quadrants is tan x > 0?

23) In which quadrants is cos x < 0?

24) In which quadrant is tan x < 0 and sin x < 0?25) Given sin

3

5 and tan < 0, find the exact values of cos and cot .

26) Solve 2 1sin for 0 360

.

27) Solve tan 3 for 180 180 .

28) Solve 2 2 1cos for 0 360 .


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29) Solve sin2 1

2 for 0 360

.

30) Solve cos 1 for 0 360

.

31) Sketch the graph of y = sin x for 0 360 .

32) Sketch the graph of y = cos x for 0 360 .

33) Sketch the graph of y = tan x for 0 360 .

34) Simplify sin .cosec

35) Simplify 9 9 2 cos

36) Simplify sin + sin .cot2

37) Prove thatsec tan

sincos

2 2

ec .

38) Prove that1

11 1

2

tan

( sin )( sin )

.

39) Evaluate x to one decimal place.

x

7.6 cm

46023’

63018’

40) Evaluate in degrees and minutes, to the nearest minute.

6.8 cm

93045’

5.4 cm

41) (a) Evaluate n correct to one decimal place.

(b) Find the area of the triangle correct to 3 significant figures.

n

102034’

2.7 m 3.5 m


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42) Find in degrees and minutes, to the nearest minute.

5.1 cm 5.3 cm

8.7cm

43) Adrian measures the angle of elevation of the top of a tower as 250 and Jane

measures the angle of elevation as 300. Jane is standing 10 metres closer to the tower than

Adrian.

300 250

10 m AJC

B

(a) Find the length of BJ to two decimal places.

(b) Hence find the height of the tower to one decimal place.

44) A ship sails for 270 km from Sydney on a bearing of 0550. It then turns and sails

for 380 km on a bearing of 1200. How far is the ship from Sydney, to the nearest km?

45)

3 cm

B

A

DE

FC

ABCDE is a regular pentagon with sides 3 cm. Point F is drawn so that

AF = BF = CF = DF = EF.

(a) Find the size of


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ANSWERS

1) tan ,sin ,cos 4

3

4

5

3

5

2) sin ,cos ,sec ,cot 95

12

12

95

12

7

7

95ec

3) sin ,cos 6

157

11

157

4) x = 510

5) 1

6) = 200

7) 1.504

8) = 76025’

9) p = 5.8

10) x = 9.2

11) = 37042’12) 6.3 metres

13) 410 km

14) 10.8 metres

15) (a) 3090 (b) 129

0

16)3

2

17) 3

18)1

2

19)1

2

20) - 3

2

21) - 1

3

22) 1st and 3rd

23) 2nd and 3rd

24) 4th

25) cos ,cot 4

5

4

3

26) =300, 150

0

27) =600, -120

0

28) =600, 120

0, 240

0, 300

0

29) =450, 135

0, 225

0, 315

0

30) =00, 360

0

31)


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y

x

1

-1

900 360027001800

32)

y

x

1

-1

900 360027001800

33) y

x

1

-1

900 360027001800


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34) 1

35) 3sin

36) cosec

37) LHS

= RHS

sec tan

sin cos

2 2

ec

38) LHS

RHS

LHS = RHS

1

11 1

2tan( sin )( sin )

39) x = 9.4 cm

40) = 52025’

41) (a) n = 4.9 m (b) 4.61 m2

42) = 113032’

43) (a) BJ = 48.49 m (b) 24.2 m44) 551 km

45) (a) 720 (b) S = 180n - 360

0 = 540

0 (when n = 5) (c) 2.6 cm

sec tan

sin

tan tan

sin

sin

cos

2 2

2 21

1

ec

1

1

1

2

2

2

tan

sec

cos

( sin )( sin )

sin

cos

1 1

1 2

2

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