Skip to content

Federal (FBISE) · Chapter test · Free

9th Class Mathematics Chapter 6 Test06. Trigonometry and Bearing

30 marks · 40 minutes · 21 questions. Covers: 06. Trigonometry and Bearing.

Your school name

9th Class Mathematics Chapter 6 Test

9th Class · Mathematics · Federal (FBISE)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 30Time: 40 minutes

Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)

  1. If a tower is 100 m high and tan θ = 1, horizontal distance from tower is:
    1. 50 m
    2. 100 m
    3. 150 m
    4. 200 m
  2. To convert degrees into radians, multiply by:
    1. π/180
    2. 180/π
    3. 60
    4. 360
  3. Bearing of South is:
    1. 090°
    2. 180°
    3. 270°
    4. 360°
  4. A bearing of 050° means:
    1. 50° clockwise from north
    2. 50° clockwise from south
    3. 50° anticlockwise from east
    4. 50° clockwise from west
  5. −3−3tan2θ=?- 3 - 3tan^2θ = ?
    1. 3cosec2θ3cosec^2θ
    2. −3cosec2θ-3cosec^2θ
    3. −3sec2θ-3sec^2θ
    4. 3sec2θ3sec^2θ
  6. One degree is equal to:
    1. 30′
    2. 60′
    3. 90′
    4. 120′
  7. Angle of elevation and corresponding angle of depression between parallel horizontals are:
    1. Complementary
    2. Equal
    3. Supplementary
    4. Always 90°
  8. Area of a sector is:
    1. rθ
    2. ½r²θ
    3. πr²
    4. 2πr
  9. Reciprocal of sin θ is:
    1. sec θ
    2. cosec θ
    3. cot θ
    4. cos θ
  10. If cos α = sin θ for acute angles, then α + θ is:
    1. 45°
    2. 60°
    3. 90°
    4. 180°

Q2. Short questions (Attempt any 6 of 8 · 6 × 2 = 12)

  1. Convert in radian. Use π= 3.1416. 60∘60^\circ
  2. Find value of θ for the following question in the interval 0≤θ≤π2 0 \leq θ \leq \frac {\pi}{2}. sec⁡2θ−2tan⁡2θ=0 {\sec^2\theta - 2\tan^2\theta} = 0
  3. Convert in radian. Write the answer in term of π. 120∘120^\circ
  4. Find radian measure of the central angle of a circular sector for the following data. A=100 cm2, ℓ=10 cmA = 100\, \text{cm}^2, \, \ell = 10\, \text{cm}
  5. Find the circular measure of the angle between the hour hand and minute hand of a clock at.02:3002 : 30
  6. Define line of sight.
  7. How many minutes are there in one degree?
  8. Prove the relation by using basic trigonometric identities. (1−sin2θ)sec2θ=1( 1 - sin^2θ ) sec^2θ = 1

Q3. Long questions (Attempt any 2 of 3 · 2 × 4 = 8)

  1. The area of a right triangle is 50 cm². One of its angles is 45⁰. Find the lengths of the sides and hypotenuse of the triangle.
  2. Prove the relation by using basic trigonometric identities. sec2θ+cosec2θ=sec2θcosec2θsec^2 θ + cosec^2 θ = sec^2 θ cosec^2 θ
  3. Two boats A and B are 5 km apart and the bearing of boat B from A is 250⁰. Draw the diagram showing relative positions of both boats, then find the bearing of boat A from boat B.