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Vidaara.orgClass 9 · Mathematics
CodeVID-M09-25-RAT-01
Trigonometric Ratios - Assignment
Chapter: Trigonometry
Topic: Trigonometric Ratios
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.
$\sin\theta=$
  • 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.
$\cos\theta=$
  • A.$\dfrac{\text{opp}}{\text{hyp}}$
  • B.$\dfrac{\text{adj}}{\text{hyp}}$
  • C.$\dfrac{\text{opp}}{\text{adj}}$
  • D.$\dfrac{\text{hyp}}{\text{adj}}$
3.
$\tan\theta=$
  • A.$\dfrac{\text{opp}}{\text{hyp}}$
  • B.$\dfrac{\text{adj}}{\text{opp}}$
  • C.$\dfrac{\text{opp}}{\text{adj}}$
  • D.$\dfrac{\text{hyp}}{\text{opp}}$
4.
$\operatorname{cosec}\theta=$
  • A.$\dfrac{1}{\cos\theta}$
  • B.$\dfrac{1}{\sin\theta}$
  • C.$\dfrac{1}{\tan\theta}$
  • D.$\sin\theta$
5.
$\tan\theta=$
  • A.$\dfrac{\sin\theta}{\cos\theta}$
  • B.$\dfrac{\cos\theta}{\sin\theta}$
  • C.$\sin\theta\cos\theta$
  • D.$\dfrac{1}{\sin\theta}$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
In a right triangle, opposite $=3$, hyp $=5$; find $\sin\theta$.
7.
adjacent $=4$, hyp $=5$; find $\cos\theta$.
8.
opposite $=3$, adjacent $=4$; find $\tan\theta$.
9.
If $\sin\theta=\tfrac35$, find $\operatorname{cosec}\theta$.
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.
If $\cos\theta=\tfrac{8}{17}$, find $\sin\theta$.
12.
If $\tan\theta=1$, find the acute angle $\theta$.
13.
If $\sin\theta=\tfrac12$, find $\cos\theta$.
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.
If $5\sin\theta=3$, find $\cos\theta$ and $\tan\theta$.

Answer Key

Section A — Multiple Choice Questions
  1. (A) $\dfrac{\text{opp}}{\text{hyp}}$
  2. (B) $\dfrac{\text{adj}}{\text{hyp}}$
  3. (C) $\dfrac{\text{opp}}{\text{adj}}$
  4. (B) $\dfrac{1}{\sin\theta}$
  5. (A) $\dfrac{\sin\theta}{\cos\theta}$
Section B — Short Answer (2 marks)
  1. $\tfrac35$.
  2. $\tfrac45$.
  3. $\tfrac34$.
  4. $\tfrac53$.
Section C — Short Answer (3 marks)
  1. $\sin=\tfrac{5}{13},\ \cos=\tfrac{12}{13},\ \tan=\tfrac{5}{12}$.
  2. $\tfrac{15}{17}$.
  3. $45^\circ$.
  4. $\tfrac{\sqrt3}{2}$.
Section D — Long Answer (5 marks)
  1. $\sin=\tfrac{8}{17},\ \cos=\tfrac{15}{17},\ \tan=\tfrac{8}{15},\ \operatorname{cosec}=\tfrac{17}{8},\ \sec=\tfrac{17}{15},\ \cot=\tfrac{15}{8}$.
  2. $\cos\theta=\tfrac45,\ \tan\theta=\tfrac34$.
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