"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-sin²x}/_{cosx}

A

2√2

B

√2

C

√2/2

D

1/2

E

**Answer:** C

Q2

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

A

18V

B

36°

C

54°

D

90°

E

**Answer:** A

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

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

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

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

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

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

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

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

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

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

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

026^{o}

B

045^{o}

C

210^{o}

D

240^{o}

E

**Answer:** D

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

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

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

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

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

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

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

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

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

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

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

Q30

Express 25° 45^{I} in decimal (Hint 1° = 60^{I})

A

25.75°

B

25.55°

C

25.45°

D

25.15°

E

**Answer:** A

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

Q32

Which of the following bearings is equivalent to S50°W?

A

040°

B

130°

C

220°

D

230°

E

**Answer:** D

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

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

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

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

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

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

2^{1}/_{2}m

C

^{5√3}/_{2 }m_{ }

D

^{10√3}/_{3 }m_{ }

E

10√3_{ }m_{ }

**Answer:** C

Q42

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

A

6400πkm

B

6400km/π

C

3200πkm

D

3200km

E

3200km/π

**Answer:** C

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

Q44

Express the true bearing of 250° as a compass bearing

A

N20°E

B

S20°E

C

N20°W

D

S70°W

E

S70°E

**Answer:** D

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

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

Q47

Two towns X and Y both on latitude 60°S have longitude 27°E and 33°W respectively. Find the nearest kilometre, the distance between X and Y measured along the parallel of latitude. [Take 2πR = 4 x 10^{4}km, where R is the radius of the earth]

A

28850km

B

16667km

C

8333km

D

6667km

E

3333km

**Answer:** A

Q48

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

A

45°, 225°

B

135°, 315°

C

45°, 315°

D

135°, 225°

E

45°, 135°

**Answer:** A

Q49

If tan x = 2^{2}/_{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

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

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}/_{3}m

B

50m

C

55√3m

D

60m

E

65m

**Answer:** C

Q52

The position of two countries: P and Q are (15^{o}N, 12^{o}E) and (65^{o}N,12^{o}E) respectively. What is the difference in latitude?

A

104°

B

100°

C

800°

D

50°

E

24°

**Answer:** D

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

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

Q55

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

A

1-k

B

k/k-1

C

k/√1-k^{2}

D

k/1-k

E

k/√k^{2}-1

**Answer:** C

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

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

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

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