Hello students, we are providing assertion reason questions for class 10. Assertion Reason questions are the new question format that is introduced in CBSE board. The resources for assertion reason questions are very less. So, to help students we have created chapterwise assertion reason questions for class 10 maths. In this article, you will find assertion reason questions for CBSE Class 10 Maths Chapter 8 Introduction to Trigonometry. It is a part of Assertion Reason Questions for CBSE Class 10 Maths Series.
| Chapter | Introduction to Trigonometry |
| Type of Questions | Assertion Reason Questions |
| Nature of Questions | Competency Based Questions |
| Board | CBSE |
| Class | 10 |
| Subject | Maths |
| Useful for | Class 10 Studying Students |
| Answers provided | Yes |
| Difficulty level | Mentioned |
| Important Link | Class 10 Maths Chapterwise Assertion Reason |
Assertion Reason Questions on Introduction to Trigonometry
Assertion and Reason Questions
Directions: Each of the following questions consists of two statements: an Assertion (A) and a Reason (R). Answer them by selecting the correct option:
(a) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true, but Reason (R) is false.
(d) Assertion (A) is false, but Reason (R) is true.
Q1. Assertion (A): The value of $\tan \theta$ increases as $\theta$ increases from $0^{\circ}$ to $90^{\circ}$.
Reason (R): As the angle increases, the ratio of opposite side to adjacent side in a right triangle increases.
Answer: Option (a) is correct.
Explanation: Since $\tan \theta=\frac{\text { opposite }}{\text { adjacent }}$, and this ratio increases with angle in a right triangle (except at $90^{\circ}$ ), both $A$ and $R$ are true and $R$ correctly explains $A$.
Difficulty Level: Moderate
Q2. Assertion (A): $\cot \theta$ is the reciprocal of $\tan \theta$, but undefined when $\tan \theta=0$.
Reason (R): The reciprocal of zero is undefined.
Answer: Option (a) is correct.
Explanation: When $\tan \theta=0, \cot \theta=\frac{1}{0}$, which is undefined. Both A and R are correct and logically connected.
Difficulty Level: Moderate
Q3. Assertion (A): If $\sin \theta=\frac{3}{5}$, then $\cos \theta=\frac{4}{5}$.
Reason $(R)$ : In a right triangle, if one leg is 3 and the hypotenuse is 5 , then the other leg must be 4 (Pythagorean triple).
Answer: Option (a) is correct.
Explanation: This is a classic example of the 3-4-5 right triangle. The identity $\sin ^2 \theta+\cos ^2 \theta=1$ also supports this.
Difficulty Level: Easy to Moderate
Q4. Assertion (A): Trigonometric ratios are independent of the size of the triangle but depend only on the angle.
Reason (R): Trigonometric ratios are derived from similar triangles which have equal angles but proportional sides.
Answer: Option (b) is correct.
Explanation: Both statements are true: ratios depend only on the angle, and similar triangles justify this. However, the reason doesn’t directly explain why the ratios are independent of triangle size.
Difficulty Level: Tough / Conceptual
Q5. Assertion (A): $\sec \theta$ and $\csc \theta$ can never be less than 1 .
Reason (R): $\cos \theta$ and $\sin \theta$ always lie between 0 and 1 for $\theta \in\left(0^{\circ}, 90^{\circ}\right)$.
Answer: Option (a) is correct.
Explanation: Since $\sec \theta=\frac{1}{\cos \theta}$ and $\csc \theta=\frac{1}{\sin \theta}$, and $\sin \theta, \cos \theta \in(0,1]$, the reciprocals are $\geq 1$.
Difficulty Level: Tough
Also check
- Some Applications of Trigonometry Class 10 Assertion Reason Questions Maths Chapter 9
- Introduction to Trigonometry Class 10 Assertion Reason Questions Maths Chapter 8
- Coordinate Geometry Class 10 Assertion Reason Questions Maths Chapter 7
- Triangles Class 10 Assertion Reason Questions Maths Chapter 6
- Arithmetic Progressions Class 10 Assertion Reason Questions Maths Chapter 5
- Quadratic Equations Class 10 Assertion Reason Questions Maths Chapter 4
- Pair of Linear Equations in Two Variables Class 10 Assertion Reason Questions Maths Chapter 3
- Polynomials Class 10 Assertion Reason Questions Maths Chapter 2
- Real Numbers Class 10 Assertion Reason Questions Maths Chapter 1
Topics from which assertion reason questions may be asked
- Trigonometric Ratios
- Values of Ratios
- Identities
Trigonometry bridges the gap between angles and lengths in right-angled triangles.
Assertion reason questions from the above given topic may be asked.
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Frequently Asked Questions (FAQs) on Introduction to Trigonometry Assertion Reason Questions Class 10
Q1: What does the chapter ‘Introduction to Trigonometry’ cover?
A1: It builds key concepts related to introduction to trigonometry and prepares you for logical reasoning-based questions.
Q2: What are assertion reason questions?
A2: These consist of two statements: an assertion and a reason. Students need to determine their correctness and relationship.
Q3: Why practice assertion reason questions in Introduction to Trigonometry?
A3: They strengthen core concepts and boost confidence in tackling tricky scenarios from introduction to trigonometry.
Q4: Are assertion reason questions part of CBSE board exams?
A4: Yes, they are included under competency-based formats to test depth of understanding.
