Last Updated on September 4, 2025 by XAM CONTENT
Hello students, we are providing case study questions for class 10 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 10 maths. In this article, you will find case study questions for CBSE Class 10 Maths Chapter 8 Introduction to Trigonometry. It is a part of Case Study Questions for CBSE Class 10 Maths Series.
| Chapter | Introduction to Trigonometry |
| Type of Questions | Case Study Questions |
| Nature of Questions | Competency Based Questions |
| Board | CBSE |
| Class | 10 |
| Subject | Maths |
| Unit | Unit 4 Geometry |
| Useful for | Class 10 Studying Students |
| Answers provided | Yes |
| Difficulty level | Mentioned |
| Important Link | Class 10 Maths Chapterwise Case Study |
Case Study Questions on Introduction to Trigonometry
Questions
Passage 1:
Here are important Class 10 Maths Case Study Questions on Introduction to Trigonometry with answers. These cover trigonometric ratios, values at standard angles, and fundamental identities, as per the latest CBSE exam pattern.
Case Study 1: Trigonometric Ratios in a Right Triangle
In a right-angled triangle $ABC$, $\angle B = 90^\circ$, $AB = 3 \, \text{cm}$, and $BC = 4 \, \text{cm}$. Using the Pythagoras theorem, $AC$ can be calculated as 5 cm.
- Find $\sin A$ and $\cos A$.
- Find $\tan A$ and $\cot A$.
- Verify that $\sin^2 A + \cos^2 A = 1$.
- Find $\sec A \cdot \cos A$.
Show Answers
Q1. $\sin A = \tfrac{BC}{AC} = \tfrac{4}{5}$, $\cos A = \tfrac{AB}{AC} = \tfrac{3}{5}$
Q2. $\tan A = \tfrac{4}{3}$, $\cot A = \tfrac{3}{4}$
Q3. $\sin^2 A + \cos^2 A = \left(\tfrac{4}{5}\right)^2 + \left(\tfrac{3}{5}\right)^2 = \tfrac{16+9}{25} = 1$ ✔
Q4. $\sec A \cdot \cos A = 1$
Case Study 2: Values of Trigonometric Ratios at Standard Angles
A teacher writes the following problem on the board: “Find the exact values of $\sin 30^\circ$, $\cos 60^\circ$, $\tan 45^\circ$, and $\sin^2 30^\circ + \cos^2 60^\circ$.”
- Evaluate $\sin 30^\circ$.
- Evaluate $\cos 60^\circ$.
- Evaluate $\tan 45^\circ$.
- Simplify $\sin^2 30^\circ + \cos^2 60^\circ$.
Show Answers
Q1. $\sin 30^\circ = \tfrac{1}{2}$
Q2. $\cos 60^\circ = \tfrac{1}{2}$
Q3. $\tan 45^\circ = 1$
Q4. $\left(\tfrac{1}{2}\right)^2 + \left(\tfrac{1}{2}\right)^2 = \tfrac{1}{4} + \tfrac{1}{4} = \tfrac{1}{2}$
Case Study 3: Trigonometric Identity in Simplification
A student tries to simplify the expression: $E = \dfrac{1 – \sin^2 \theta}{\cos^2 \theta}$ for some angle $\theta$.
- Simplify $1 – \sin^2 \theta$ using a trigonometric identity.
- Hence, simplify $E$.
- Find the value of $E$ when $\theta = 30^\circ$.
- Which identity is used here?
Show Answers
Q1. $1 – \sin^2 \theta = \cos^2 \theta$
Q2. $E = \dfrac{\cos^2 \theta}{\cos^2 \theta} = 1$
Q3. For $\theta = 30^\circ$, $E = 1$
Q4. Identity used: $\sin^2 \theta + \cos^2 \theta = 1$
Also check
- Introduction to Trigonometry Class 10 Case Study Questions Maths Chapter 8
- Coordinate Geometry Class 10 Case Study Questions Maths Chapter 7
- Triangles Class 10 Case Study Questions Maths Chapter 6
- Arithmetic Progressions Class 10 Case Study Questions Maths Chapter 5
- Quadratic Equations Class 10 Case Study Questions Maths Chapter 4
- Pair of Linear Equations in Two Variables Class 10 Case Study Questions Maths Chapter 3
- Polynomials Class 10 Case Study Questions Maths Chapter 2
- Real Numbers Class 10 Case Study Questions Maths Chapter 1
Topics from which case study questions may be asked
- Motivation for Studying Arithmetic Progression
- Derivation of the nth Term of an A.P.
- Derivation of the Sum of the First n Terms of an A.P.
- Applications of A.P. in Solving Daily Life Problems
Case study questions based on above topics may be asked.
Understanding Introduction to Trigonometry
Trigonometric Ratios
In a right-angled triangle, the trigonometric ratios for an acute angle θ are defined as:
sin θ = Perpendicular / Hypotenuse
cos θ = Base / Hypotenuse
tan θ = Perpendicular / Base
cot θ = Base / Perpendicular
sec θ = Hypotenuse / Base
cosec θ = Hypotenuse / Perpendicular
Values of Trigonometric Ratios at Standard Angles
Important values to remember:
At 0°, 30°, 45°, 60°, 90°:
sin θ → 0, 1/2, 1/√2, √3/2, 1
cos θ → 1, √3/2, 1/√2, 1/2, 0
tan θ → 0, 1/√3, 1, √3, ∞
Note: The value of sin θ or cos θ never exceeds 1, while sec θ and cosec θ are always ≥ 1.
Trigonometric Identities
Three fundamental identities are:
1. sin²θ + cos²θ = 1
2. 1 + tan²θ = sec²θ
3. 1 + cot²θ = cosec²θ
Relations Between Ratios
tan θ = sin θ / cos θ
cot θ = cos θ / sin θ
sec θ = 1 / cos θ
cosec θ = 1 / sin θ
Key Points to Remember
1. Trigonometric ratios depend only on the angle, not on the actual lengths of the triangle sides.
2. Standard angles (0°, 30°, 45°, 60°, 90°) and their ratio values must be memorized.
3. Identities are used to simplify and prove trigonometric expressions.
4. tan θ and cot θ are undefined for θ = 90° and θ = 0° respectively.
Frequently Asked Questions (FAQs) on Introduction to Trigonometry Case Study
Q1: What is trigonometry?
A1: Trigonometry is a branch of mathematics that studies the relationships between the angles and sides of right-angled triangles. It is widely used in geometry, physics, engineering, and real-life applications like heights and distances.
Q2: Why is trigonometry introduced in Class 10?
A2: In Class 10, students learn the basics of trigonometric ratios, their values at standard angles, and fundamental identities. These concepts form the foundation for advanced mathematics and its applications in higher studies.
Q3: What are the six trigonometric ratios?
A3: The six trigonometric ratios are: sine (sin), cosine (cos), tangent (tan), cosecant (cosec), secant (sec), and cotangent (cot). They are defined using the sides of a right-angled triangle with respect to an acute angle.
Q4: What are trigonometric identities?
A4: Trigonometric identities are equations that are true for all values of the angle θ. The three fundamental identities are:
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
Q5: What are common mistakes students make in trigonometry?
A5: Common mistakes include:
Confusing sin θ with cos θ values.
Forgetting that tan θ = sin θ / cos θ.
Not remembering that tan 90° is undefined.
Mixing up the values of ratios at standard angles (like 30°, 45°, 60°).
Q7: Are there any online resources or tools available for practicing “Introduction to Trigonometry” case study questions?
A7: We provide case study questions for CBSE Class 10 Maths on our website. Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.
