Trigonometry Generix Content - Trigonometry
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"Trigonometry" question number distribution across years
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WAEC questions for "Mathematics :: Trigonometry"
Q1

Given that tan x = , where 0 ≤ x ≤ 90, 1-sinx/cosx

A

2√2

B

√2

C

√2/2

D

1/2

E

Answer: C

Trigonometry
Q2

If sin3y = cos2y and 0 ≤ y ≤ 90, find the value of y

A

18V

B

36

C

54

D

90

E

Answer: A

Trigonometry
Q3

Given that sin 60 = √3/2 and cos 60 = 1/2 evaluate: 1- sin 60/ 1+ cos 60

A

2 + √3/3

B

1 - √3/3

C

1 + √3 /3

D

2 - √3/3

E

Answer: D

Trigonometry
Q4

Find the bearing of X from Y

A

300

B

240

C

120

D

60

E

Answer: B

Trigonometry
Q5

If /XY/ = 50m, how far cast of X is Y?

A

25.5m

B

40.6m

C

40.8m

D

43.3m

E

Answer: D

Trigonometry
Q6

If tan x = 1, evaluate sinx + cosx, leaving your answer in the surd form.

A

2√2

B

1/2√2

C

√2

D

2

E

Answer: C

Trigonometry
Q7

If cos (x+25) = sin 45, find the value of x.

A

20

B

30

C

45

D

60

E

Answer: A

Trigonometry
Q8

In the diagram, |LN| = 4cm, <LNM = 90° and tan y = 2/3. What is the area of the ΔLMN?

 

A

24cm²

B

12cm²

C

10cm²

D

6cm²

E

Answer: B

Trigonometry
Q9

Q is 32km away from P on a bearing 042 and R is 25km from P on a bearing of 132. Calculate the bearing of R from Q.

A

122

B

184

C

190

D

226

E

Answer: B

Trigonometry
Q10

In the diagram, |PQ| = 4cm, |QR| = 6cm, |RS| = 12cm and <QRS = 90°. Find the value of x. 

A

27

B

26

C

18

D

13

E

Answer: D

Trigonometry
Q11

The bearing of a bearing of a point P from another point Q is 310. If |PQ| = 20m, hw far west of Q is P?

A

128.6m

B

153.2m

C

167.8m

D

187.9m

E

Answer: B

Trigonometry
Q12

if tan y = 0.404, where y is acute, find cos 2y

A

0.035

B

0.719

C

0.808

D

0.927

E

Answer: B

Trigonometry
Q13

In the diagram P, Q and R are three points in a plane such that the bearing of R from Q is 110 and the bearing of Q from P is 050. Find angle PQR

A

60

B

70

C

120

D

160

E

Answer: C

Trigonometry
Q14

A ladder 16m long leans against an electric pole. If the ladder makes and angle of 65 with the ground, how r

far up the electric pole does its top reach?

A

6.8m

B

14.5m

C

17.1m

D

34.3m

E

Answer: B

Trigonometry
Q15

From a point P,R is 5km due west and 12km due south. Find the distance between P and R

A

5km

B

12km

C

13km

D

17km

E

Answer: C

Trigonometry
Q16

From a point R, 300m north of P, a man walks eastwards to a place Q which is 600m from P. Find the bearing of P from Q correct to the nearest degree.

A

026o

B

045o

C

210o

D

240o

E

Answer: D

Trigonometry
Q17

The angle of evevation of the top of a cliff 15 meters high from a landmark is 60. How far is the landmark from the foot of the cliff? Leave your answer in surd form.

A

15√3 m

B

15√2 m

C

10√3 m

D

5√3 m

E

Answer: D

Trigonometry
Q18

Given that sin (5x - 28) = cos (3x - 50), 0 < x < 90, find the value of x.

A

14

B

21

C

32

D

39

E

Answer: B

Trigonometry
Q19

The angle of elevation of the top of a tower from a ppoint on the ground which is 36m away from the foot of the tower is 30. Calculate the height of the tower.

A

62.35m

B

20.78m

C

18.00m

D

10.39m

E

Answer: B

Trigonometry
Q20

A point X is on the bearing 342 from a point Y. What is the bearing of Y from X?

A

342

B

252

C

198

D

162

E

Answer: D

Trigonometry
Q21

A point on the ground is 5m away from the foot of a vertical wall 7m high. Calculate, correct to the nearest degree, the angle of depression of the point from the top of the wall.

A

36

B

44

C

46

D

54

E

Answer: D

Trigonometry
Q22

A ladder, 6cm long, leans against a vertical wall at an angle 53 to the horizontal. How high up the wall does the ladder reach?

A

3.611 m

B

4.521 m

C

4.792 m

D

7.962 m

E

Answer: C

Trigonometry
Q23

Evaluate Cos 45 Cos 30 - Sin 45 Sin 30 leaving the answer in surd form

A

√2 - 1/2

B

√3 - √2/4

C

√6 - √2/2

D

√6 - √2/4

E

Answer: D

Trigonometry
Q24

The bearing of P from Q is x, where 270 < x < 360. Find the bearing of Q from P.

A

(x - 90)

B

(x - 270)

C

(x - 135)

D

(x - 180)

E

Answer: D

Trigonometry
Q25

Points X, Y and Z are located in the same horizontal plane such that Y is 12km north of X and Z is on a bearing of 270 from X. If |XZ| = 6km, calculate, correct to one decimal place, |YZ|.

A

18km

B

13.4km

C

13km

D

10.4km

E

Answer: B

Trigonometry
Q26

From the diagram, find the bearing of Q from P.

A

236

B

214

C

146

D

124

E

Answer: A

Trigonometry
Q27

The angle of depression of a point Q from a vertical tower PR, 30m high, is 40. If the foot P of the tower is on the same horizontal level as Q, find correct to 2 decimal places, |PQ|.

A

35.75m

B

25.00m

C

22.98m

D

19.28m

E

Answer: A

Trigonometry
Q28

The bearing S40E is the same as

A

040

B

050

C

130

D

140

E

Answer: D

Trigonometry
Q29

Three obersevation posts P, Q and R are such that Q is due east of P and R is due north of Q. If /PQ/ = 5km and /PR/ = 10km, find /QR/

A

5.0km

B

7.5km

C

7.6km

D

8.7km

E

Answer: D

Trigonometry
Q30

Express 25 45I in decimal (Hint 1 = 60I)

A

25.75

B

25.55

C

25.45

D

25.15

E

Answer: A

Trigonometry
Q31

In the diagram AB is a vertical pole and BC is horizontal. If /AC/ = 10m and /BC/ = 5m. Calculate the angle of depression of C from A

A

63

B

60

C

45

D

27

E

Answer: B

Trigonometry
Q32

Which of the following bearings is equivalent to S50W?

A

040

B

130

C

220

D

230

E

Answer: D

Trigonometry
Q33

How far is Kofi from the building?

A

4√2km

B

8km

C

8√2km

D

16km

E

Answer: C

Trigonometry
Q34

Find the bearing of Kofi from the building?

A

315

B

270

C

225

D

135

E

Answer: C

Trigonometry
Q35

If tan x = 1/√3 find cos x - sin x such that 0≤x≤90,

A

√3+1/2

B

2/√3 + 1

C

√3-1/2

D

2/√3 - 1

E

Answer: C

Trigonometry
Q36

From the top a cliff 20m high, a boat can be sighted at sea 75m from the foot of the cliff. Calculate the angle of depression of the boat from the top of the cliff.

A

14.9

B

15.5

C

74.5

D

75.1

E

Answer: A

Trigonometry
Q37

The diagram shows the position of three ships A, B and C at sea. B is due north of C such that /AB/ = /BC/ and the bearing of B from A = 040. What is the bearing of A from C?


A

040

B

070

C

110

D

290

E

Answer: D

Trigonometry
Q38

A pole of lenght L leans aganist a vertical wall so that it makes an angle of 60 with the horizontal ground. If the top of the pole is 8m above the ground, calculate L

A

16√3m

B

4√3m

C

√3m/16

D

16√3m/3

E

Answer: D

Trigonometry
Q39

If sin (x+30) = cos 40, find X

A

10

B

20

C

50

D

60

E

90

Answer: B

Trigonometry
Q40

Find the value of x if Cos x = 5/8 for 0 ≤ x ≤ 180

A

141.3

B

128.7

C

51.3

D

48.7

E

38.7

Answer: C

Trigonometry
Q41

A aldder 5m long against a wall such that its foot makes an angle of 30 with the horizontal. How far is foot of the ladder from the wall?

A

5√2/3 m

B

21/2m

C

5√3/2 m

D

10√3/3 m

E

10√3 m

Answer: C

Trigonometry
Q42

Two points P and Q are on longitude 67W. Their latitude differ by 90. Calculate their distance apart in terms ofπ. (Take radius of the earth = 6400km)

A

6400πkm

B

6400km/π

C

3200πkm

D

3200km

E

3200km/π

Answer: C

Trigonometry
Q43

The angle of elevation of a point T on a tower from a point U on the horizantal ground is 30. If TU = 54cm, how high is T above the horizonal ground?

A

108m

B

72m

C

46.3m

D

31.2m

E

27m

Answer: E

Trigonometry
Q44

Express the true bearing of 250 as a compass bearing

A

N20E

B

S20E

C

N20W

D

S70W

E

S70E

Answer: D

Trigonometry
Q45

If sinθ = -1/2 , find all th evalues of θ between 0 and 360

A

120,240

B

120, 180

C

210, 300

D

210, 330

E

300,360

Answer: D

Trigonometry
Q46

Cos 65 has the same value as

A

Sin 65

B

Cos 25

C

Cos 115

D

Cos 205

E

Cos 295

Answer: E

Trigonometry
Q47

Two towns X and Y both on latitude 60S have longitude 27E and 33W respectively. Find the nearest kilometre, the distance between X and Y measured along the parallel of latitude. [Take 2πR = 4 x 104km, where R is the radius of the earth]

A

28850km

B

16667km

C

8333km

D

6667km

E

3333km

Answer: A

Trigonometry
Q48

If sin θ = cos θ, for 0≤ 0≤ 360, find the value ofθ

A

45, 225

B

135, 315

C

45, 315

D

135, 225

E

45, 135

Answer: A

Trigonometry
Q49

If tan x = 22/5, find the value of sin x; 0 ≤ x ≤ 90

A

5/13

B

5/12

C

144/169

D

12/13

E

13/12

Answer: D

Trigonometry
Q50

A town P is 150km from a town Q in the direction 050. What is the bearing of Q from P?

A

050

B

130

C

230

D

270

E

310

Answer: C

Trigonometry
Q51

The angle of elevation of the top X of a vertical pole from a point P on a level ground is 60. The distance from a point P to the foot of the pole is 55cm. Without using tables, find the height of the pole.

A

50/3m

B

50m

C

55√3m

D

60m

E

65m

Answer: C

Trigonometry
Q52

The position of two countries: P and Q are (15oN, 12oE) and (65oN,12oE) respectively. What is the difference in latitude?

A

104

B

100

C

800

D

50

E

24

Answer: D

Trigonometry
Q53

Without using tables, find the value of (sin 20/ cos 70) + ( cos 25 / sin 65)

A

2

B

1

C

0

D

-1

E

-2

Answer: A

Trigonometry
Q54

The bearing of two points Q and R from a point P are 030 and 120 respectively. If /PQ? = 12m and /PR/ = 5m, find the distance QR.

A

13m

B

11m

C

9m

D

7m

E

5m

Answer: A

Trigonometry
Q55

If sin θ = k, find tan θ, 0° ≤ θ ≤ 90°

A

1-k

B

k/k-1

C

k/√1-k2

D

k/1-k

E

k/√k2-1

Answer: C

Trigonometry
Q56

A ladder 6m long leans against a vertical wall so that it makes an angle of 60 with the wall. Calculate the diatance of the foot of the ladder from the wall.

A

3m

B

6m

C

2√3m

D

3√3m

E

6√3m

Answer: E

Trigonometry
Q57

The bearing of Q from P is 122, what is the bearing of P from Q?

A

212

B

238

C

248

D

292

E

302

Answer: E

Trigonometry
Q58

Cos 57 has the same value as

A

sin 213

B

cos 303

C

cos 147

D

cos 123

E

cos 237

Answer: B

Trigonometry
Q59

A plane flies 90km on a bearing 030 and then flies 150km due east. How far east of the starting point is the plane?

A

120km

B

165km

C

195km

D

(150+45 √3)km

E

240km

Answer: A

Trigonometry
Q60

If sin x = cos 50, then x equals

A

40

B

45

C

50

D

90

E

130

Answer: A

Trigonometry