Vidaara.orgClass 11 · Mathematics
CodeVID-M11-03-CT
Trigonometric Functions — Full Chapter Test
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- This is a full-length test covering the whole chapter — every topic is included.
- 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.
$\sin^2\theta+\cos^2\theta=$
- A.$0$
- B.$1$
- C.$2$
- D.$\tan^2\theta$
3.
The general solution of $\sin\theta=0$ is:
- A.$n\pi$
- B.$2n\pi$
- C.$(2n+1)\tfrac{\pi}{2}$
- D.$n\pi+\tfrac{\pi}{2}$
4.
$\tfrac{\pi}{4}$ radian in degrees is:
- A.$30^\circ$
- B.$45^\circ$
- C.$60^\circ$
- D.$90^\circ$
5.
$\cos 60^\circ=$
- A.$\tfrac{\sqrt3}{2}$
- B.$\tfrac12$
- C.$1$
- D.$0$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Convert $90^\circ$ to radians.
7.
Find $\sin 30^\circ+\cos 60^\circ$.
8.
Solve $\sin\theta=\tfrac12$ (general solution).
9.
Convert $\tfrac{\pi}{3}$ radian to degrees.
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.
Find the value of $\sin 75^\circ$.
12.
Solve $\cos\theta=-\tfrac12$ (general solution).
13.
Convert $40^\circ20'$ to radians.
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.
Prove that $\dfrac{1+\cos\theta}{\sin\theta}+\dfrac{\sin\theta}{1+\cos\theta}=2\csc\theta$.
Answer Key
Section A — Multiple Choice Questions
- (A) $\pi$
- (B) $1$
- (A) $n\pi$
- (B) $45^\circ$
- (B) $\tfrac12$
Section B — Short Answer (2 marks)
- $\tfrac{\pi}{2}$.
- $1$.
- $\theta=n\pi+(-1)^n\tfrac{\pi}{6}$.
- $60^\circ$.
Section C — Short Answer (3 marks)
- $\tfrac{14\pi}{3}$ cm.
- $\tfrac{\sqrt6+\sqrt2}{4}$.
- $\theta=2n\pi\pm\tfrac{2\pi}{3}$.
- $\tfrac{121\pi}{540}$.
Section D — Long Answer (5 marks)
- $\tfrac{\pi}{9},\ \tfrac{\pi}{3},\ \tfrac{5\pi}{9}$ (i.e. $20^\circ,60^\circ,100^\circ$).
- Both sides reduce to $2\csc\theta$.
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