Vidaara.orgClass 9 · Mathematics
CodeVID-M9-25-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.$\dfrac{\text{opp}}{\text{hyp}}$
- B.$\dfrac{\text{adj}}{\text{hyp}}$
- C.$\dfrac{\text{opp}}{\text{adj}}$
- D.$\dfrac{\text{hyp}}{\text{opp}}$
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.
$\sin^2\theta+\cos^2\theta=$
- A.$0$
- B.$1$
- C.$2$
- D.$\tan\theta$
5.
$\cos\theta=$
- A.$\dfrac{\text{opp}}{\text{hyp}}$
- B.$\dfrac{\text{adj}}{\text{hyp}}$
- C.$\dfrac{\text{opp}}{\text{adj}}$
- D.$\dfrac{\text{hyp}}{\text{adj}}$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
In a right triangle, opposite $=3$, hyp $=5$; find $\sin\theta$.
7.
Find $\sin 45^\circ$.
8.
Express $\sin 70^\circ$ as a cosine.
9.
If $\sin\theta=\tfrac35$, find $\cos\theta$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
In a $5,12,13$ right triangle, find $\sin,\cos,\tan$ of the angle opposite the side $5$.
11.
Evaluate $\sin 30^\circ+\cos 60^\circ$.
12.
Evaluate $\dfrac{\sin 35^\circ}{\cos 55^\circ}$.
13.
Verify $\sin^2 30^\circ+\cos^2 30^\circ=1$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
In a right triangle, the side opposite $\theta$ is $8$ and the hypotenuse is $17$. Find all six trigonometric ratios of $\theta$.
15.
Evaluate $\sin 60^\circ\cos 30^\circ+\cos 60^\circ\sin 30^\circ$.
Answer Key
Section A — Multiple Choice Questions
- (A) $\dfrac{\text{opp}}{\text{hyp}}$
- (A) $\tfrac12$
- (B) $\cos\theta$
- (B) $1$
- (B) $\dfrac{\text{adj}}{\text{hyp}}$
Section B — Short Answer (2 marks)
- $\tfrac35$.
- $\tfrac{1}{\sqrt2}$.
- $\cos 20^\circ$.
- $\tfrac45$.
Section C — Short Answer (3 marks)
- $\sin=\tfrac{5}{13},\ \cos=\tfrac{12}{13},\ \tan=\tfrac{5}{12}$.
- $1$.
- $1$.
- $\tfrac14+\tfrac34=1$.
Section D — Long Answer (5 marks)
- $\sin=\tfrac{8}{17},\ \cos=\tfrac{15}{17},\ \tan=\tfrac{8}{15},\ \operatorname{cosec}=\tfrac{17}{8},\ \sec=\tfrac{17}{15},\ \cot=\tfrac{15}{8}$.
- $1$.
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