TRIGONOMETRY AND BEARING

1

Zara is finding the length of an arc of a circle with radius 10 cm and central angle 90°. What is the arc length? (Use π = 3.14)

A 15.7 cm B 31.4 cm C 7.85 cm D 20 cm

2

What is the sector angle of a circle if the arc length is 10 cm and the radius is 5 cm?

A 2 radians B 0.5 radians C 50 radians D 15 radians

3

Sadia is solving the identity 1 + cot²θ. Which trigonometric function is it equal to?

A sec²θ B csc²θ C tan²θ D cos²θ

4

Convert 120° to radians.

A 2π/3 B π/3 C 2π/5 D 3π/4

5

Nadia is converting π/4 radians to degrees. What is the angle in degrees?

A 30° B 45° C 60° D 90°

6

Saad is converting 3π/2 radians to degrees. What is the angle?

A 270° B 180° C 360° D 90°

7

If tan θ = 1, what is the value of θ in degrees (0° ≤ θ ≤ 90°)?

A 45° B 30° C 60° D 90°

8

Danish is finding the area of a sector with radius 21 cm and angle 120°. What is the area? (Use π = 22/7)

A 462 cm² B 231 cm² C 924 cm² D 154 cm²

9

Nashit is converting 5π/6 radians to degrees. What is the angle?

A 150° B 120° C 135° D 210°

10

In a right-angled triangle, if sin θ = 0.6, then cos θ is approximately:

A 0.8 B 0.4 C 1.2 D 0.2

11

A tower casts a shadow 20 m long when the sun's elevation is 30°. How tall is the tower?

A 20/√3 m B 20√3 m C 10 m D 40 m

12

Aqib is converting 7π/4 radians to degrees. What is the angle?

A 315° B 225° C 270° D 300°

13

Nimra is converting 135° to radians. What is the value?

A 3π/4 B 5π/4 C 2π/3 D 7π/6

14

What is the angle of depression if a person looks down from a height to an object on the ground?

A The angle between the line of sight and the horizontal B The angle between the vertical and the line of sight C The angle at the object D The angle at the observer's feet

15

Amina is converting 240° to radians. What is the value?

A 4π/3 B 3π/4 C 5π/3 D 2π/3

16

What is the angle of depression from a point A (height 100 m) to point B on the ground if the horizontal distance is 100 m?

A 45° B 30° C 60° D 90°

17

Rabia is standing 15 m from a building. The angle of elevation to the top is 45°. How tall is the building?

A 15 m B 15√2 m C 30 m D 7.5 m

18

What is the arc length of a sector with radius 10 cm and angle π/2 radians?

A 5π cm B 10π cm C 20π cm D π cm

19

What is the value of sec 60°?

A 2 B 1/2 C √3/2 D 2/√3

20

Mariam is given a right triangle with opposite side 8 and hypotenuse 17. What is cos θ?

A 15/17 B 8/17 C 8/15 D 17/15

21

Saba is simplifying cot θ. Which ratio is correct?

A cos θ / sin θ B sin θ / cos θ C 1 / sin θ D 1 / cos θ

22

Farah is finding the bearing of B from A if B is 10 km south and 10 km west of A. What is the bearing?

A 225° B 135° C 315° D 045°

23

In a triangle, if tan θ = 4/3, what is sin θ?

A 4/5 B 3/5 C 5/4 D 3/4

24

Arslan is given a right triangle with adjacent side 7 and hypotenuse 25. What is sin θ?

A 24/25 B 7/25 C 7/24 D 25/24

25

What is the value of sin 45°?

A √2/2 B 1/2 C √3/2 D 1