Vidaara.orgClass 10 · Mathematics
CodeVID-M10-09-CT
Trigonometry — 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.
$\sin\theta=$
- A.$\tfrac{\text{adj}}{\text{hyp}}$
- B.$\tfrac{\text{opp}}{\text{hyp}}$
- C.$\tfrac{\text{opp}}{\text{adj}}$
- D.$\tfrac{\text{hyp}}{\text{opp}}$
2.
$\sin 30^\circ=$
- A.$\tfrac12$
- B.$\tfrac{\sqrt3}{2}$
- C.$1$
- D.$0$
3.
$\sin(90^\circ-\theta)=$
- A.$\sin\theta$
- B.$\cos\theta$
- C.$\tan\theta$
- D.$\cot\theta$
4.
$\cos\theta=$
- A.$\tfrac{\text{adj}}{\text{hyp}}$
- B.$\tfrac{\text{opp}}{\text{hyp}}$
- C.$\tfrac{\text{opp}}{\text{adj}}$
- D.$\tfrac{1}{\sin\theta}$
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.
If $\sin\theta=\tfrac35$ ($\theta$ acute), find $\cos\theta$.
7.
Evaluate $\sin 30^\circ+\cos 60^\circ$.
8.
Evaluate $\dfrac{\sin 35^\circ}{\cos 55^\circ}$.
9.
If $\tan\theta=1$, find $\theta$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
If $\tan\theta=\tfrac43$, find $\sin\theta$ and $\cos\theta$.
11.
Evaluate $\sin 30^\circ\cos 60^\circ+\cos 30^\circ\sin 60^\circ$.
12.
Evaluate $\dfrac{\sin 18^\circ}{\cos 72^\circ}+\dfrac{\cos 15^\circ}{\sin 75^\circ}$.
13.
Show that $1-\cos^2\theta=\sin^2\theta$ and verify at $\theta=30^\circ$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Prove that $\dfrac{\sin\theta}{1+\cos\theta}+\dfrac{1+\cos\theta}{\sin\theta}=2\csc\theta$.
15.
Evaluate $2\sin^2 30^\circ-3\cos^2 45^\circ+\tan^2 60^\circ$.
Answer Key
Section A — Multiple Choice Questions
- (B) $\tfrac{\text{opp}}{\text{hyp}}$
- (A) $\tfrac12$
- (B) $\cos\theta$
- (A) $\tfrac{\text{adj}}{\text{hyp}}$
- (B) $\tfrac12$
Section B — Short Answer (2 marks)
- $\tfrac45$.
- $1$.
- $1$.
- $45^\circ$.
Section C — Short Answer (3 marks)
- $\sin\theta=\tfrac45,\ \cos\theta=\tfrac35$.
- $1$.
- $2$.
- Both equal $\tfrac14$.
Section D — Long Answer (5 marks)
- $=2\csc\theta$.
- $2$.
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