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Vidaara.orgClass 11 · Mathematics
CodeVID-M11-03-ANG-01
Angles & Radian Measure — Assignment
Chapter: Trigonometric Functions
Topic: Angles and Radian Measure
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
$180^\circ=$ ___ radians.
  • A.$\pi$
  • B.$2\pi$
  • C.$\tfrac{\pi}{2}$
  • D.$\tfrac{\pi}{4}$
2.
$\tfrac{\pi}{4}$ radian in degrees is:
  • A.$30^\circ$
  • B.$45^\circ$
  • C.$60^\circ$
  • D.$90^\circ$
3.
The arc-length formula is:
  • A.$l=r\theta$
  • B.$l=\tfrac12 r^2\theta$
  • C.$l=r/\theta$
  • D.$l=2\pi r$
4.
$270^\circ$ in radians is:
  • A.$\tfrac{3\pi}{2}$
  • B.$\tfrac{\pi}{2}$
  • C.$\pi$
  • D.$2\pi$
5.
$1^\circ$ in radians is:
  • A.$\tfrac{\pi}{180}$
  • B.$\tfrac{180}{\pi}$
  • C.$\pi$
  • D.$\tfrac{\pi}{90}$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Convert $90^\circ$ to radians.
7.
Convert $\tfrac{\pi}{3}$ radian to degrees.
8.
Find the arc length when $r=7$ and $\theta=2$ radians.
9.
Convert $210^\circ$ to radians.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the arc length of a circle of radius $14$ cm subtending $\theta=\tfrac{\pi}{3}$ at the centre.
11.
Convert $40^\circ20'$ to radians.
12.
Find the degree measure of an angle of $5$ radians.
13.
Find the length of the arc subtending $30^\circ$ at the centre of a circle of radius $12$ cm.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
The angles of a triangle are in AP and the greatest is $5$ times the least. Find the three angles in radians.
15.
In a circle of radius $5$ cm an arc subtends $1.2$ radians at the centre. Find the arc length and the area of the corresponding sector.

Answer Key

Section A — Multiple Choice Questions
  1. (A) $\pi$
  2. (B) $45^\circ$
  3. (A) $l=r\theta$
  4. (A) $\tfrac{3\pi}{2}$
  5. (A) $\tfrac{\pi}{180}$
Section B — Short Answer (2 marks)
  1. $\tfrac{\pi}{2}$.
  2. $60^\circ$.
  3. $14$ units.
  4. $\tfrac{7\pi}{6}$.
Section C — Short Answer (3 marks)
  1. $\tfrac{14\pi}{3}$ cm.
  2. $\tfrac{121\pi}{540}$.
  3. $\left(\dfrac{900}{\pi}\right)^\circ$.
  4. $2\pi$ cm.
Section D — Long Answer (5 marks)
  1. $\tfrac{\pi}{9},\ \tfrac{\pi}{3},\ \tfrac{5\pi}{9}$ (i.e. $20^\circ,60^\circ,100^\circ$).
  2. Arc $=6$ cm; sector area $=15$ cm$^2$.
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