Class 10 Maths Chapter 8 Introduction to Trigonometry MCQs Quiz

Are you struggling to remember the formulas and concepts of Chapter 8, ‘Introduction to Trigonometry’? Do trigonometric ratios like sin, cos, and tan seem difficult? Your search for help ends here! We bring you the Class 10 Maths Chapter 8 Introduction to Trigonometry MCQs Quiz. This free online test will help you understand the basic principles of trigonometry and commit the formulas to memory. Let’s give your board exam preparation a strong foundation with this essential Trigonometry quiz!

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Introduction to Trigonometry MCQs Quiz

Click the Start button to begin the quiz and attempt all questions within the given time. Read each MCQ carefully, select the correct option, and move forward to complete the quiz. Your score will appear at the end to help you check your preparation level..

Q1: In a right triangle ABC, with angle B being the right angle, if AB = 12 cm and BC = 5 cm, what is the value of sin A?

A: \( \frac{5}{13} \)
B: \( \frac{12}{13} \)
C: \( \frac{5}{12} \)
D: \( \frac{12}{5} \)

Explanation: In a right triangle, sin A = opposite side / hypotenuse = BC / AC. AC = √(AB² + BC²) = √(12² + 5²) = √(144+25) = √169 = 13 cm. Therefore sin A = 5/13.

Q2: If sin θ = \( \frac{3}{5} \), then what is the value of cos θ?

A: \( \frac{4}{5} \)
B: \( \frac{5}{4} \)
C: \( \frac{3}{4} \)
D: \( \frac{5}{3} \)

Explanation: Using the trigonometric identity sin²θ + cos²θ = 1, cos²θ = 1 – sin²θ = 1 – (3/5)² = 1 – 9/25 = 16/25. Therefore cos θ = √(16/25) = 4/5 (since θ is an acute angle).

Q3: What is the value of tan 45°?

A: 0
B: 1
C: \( \frac{1}{\sqrt{2}} \)
D: \( \sqrt{3} \)

Explanation: tan 45° = 1, this is a standard trigonometric value.

Q4: What is the value of the expression \( \sin^2 30^\circ + \cos^2 30^\circ \)?

A: 0
B: 1
C: \( \frac{1}{2} \)
D: \( \frac{\sqrt{3}}{2} \)

Explanation: The trigonometric identity sin²θ + cos²θ = 1 holds for any angle θ. Here θ = 30°, so the value is 1.

Q5: If sec θ = \( \frac{13}{5} \), then what is the value of tan θ?

A: \( \frac{12}{5} \)
B: \( \frac{5}{12} \)
C: \( \frac{13}{12} \)
D: \( \frac{12}{13} \)

Explanation: sec θ = hypotenuse / base = 13/5. Consider a right triangle with hypotenuse = 13, base = 5, then perpendicular = √(13² – 5²) = √(169 – 25) = √144 = 12. tan θ = perpendicular / base = 12/5.

Q6: What is the value of \( \frac{\sin 30^\circ + \cos 60^\circ}{1 + \sin 60^\circ + \cos 30^\circ} \)?

A: \( \frac{1}{2} \)
B: \( \frac{1}{\sqrt{3}} \)
C: \( \frac{1}{1+\sqrt{3}} \)
D: \( \frac{1}{3} \)

Explanation: sin 30° = 1/2, cos 60° = 1/2, so numerator = 1/2 + 1/2 = 1. sin 60° = √3/2, cos 30° = √3/2, so denominator = 1 + √3/2 + √3/2 = 1 + √3. Therefore the expression = 1/(1+√3).

Q7: If θ = 30°, then what is the value of \( 2 \sin \theta \cos \theta \)?

A: \( \frac{1}{2} \)
B: \( \frac{\sqrt{3}}{2} \)
C: 1
D: 0

Explanation: 2 sin θ cos θ = sin 2θ. Here θ = 30°, so 2θ = 60°. sin 60° = √3/2.

Q8: Using the identity \( \sec^2 \theta = 1 + \tan^2 \theta \), if tan θ = 1, what is the value of sec θ?

A: 0
B: 1
C: \( \sqrt{2} \)
D: 2

Explanation: tan θ = 1, then sec²θ = 1 + tan²θ = 1 + 1 = 2. Therefore sec θ = √2.

Q9: If sin (A + B) = 1 and cos (A – B) = 1, where A and B are acute angles, what are the values of A and B?

A: A = 45°, B = 45°
B: A = 60°, B = 30°
C: A = 30°, B = 60°
D: A = 0°, B = 90°

Explanation: sin (A+B) = 1 ⇒ A+B = 90°. cos (A-B) = 1 ⇒ A-B = 0°. Solving these equations, A = 45° and B = 45°.

Q10: What is the value of the expression \( \frac{\tan 60^\circ – \tan 30^\circ}{1 + \tan 60^\circ \tan 30^\circ} \)?

A: \( \frac{1}{\sqrt{3}} \)
B: 1
C: \( \sqrt{3} \)
D: 0

Explanation: This is the formula for tan (60° – 30°), so tan (60° – 30°) = tan 30° = 1/√3.

Q11: What is the value of cosec 30°?

A: 1
B: 2
C: \( \frac{1}{2} \)
D: \( \sqrt{2} \)

Explanation: cosec 30° = 1 / sin 30° = 1 / (1/2) = 2.

Q12: If \( \sin \theta = \frac{12}{13} \), then what is the value of \( \cot \theta \)?

A: \( \frac{12}{5} \)
B: \( \frac{5}{12} \)
C: \( \frac{13}{12} \)
D: \( \frac{13}{5} \)

Explanation: sin θ = 12/13, so in a right triangle, opposite side = 12, hypotenuse = 13, adjacent side = √(13² – 12²) = √(169 – 144) = √25 = 5. cot θ = adjacent side / opposite side = 5/12.

Q13: What is the value of \( \cos 48^\circ – \sin 42^\circ \)?

A: 1
B: 0
C: -1
D: \( \frac{1}{2} \)

Explanation: cos 48° = sin (90° – 48°) = sin 42°. Therefore cos 48° – sin 42° = sin 42° – sin 42° = 0.

Q14: If sec A = x, then what is the value of tan A? (Assume A is an acute angle.)

A: \( \sqrt{x^2 – 1} \)
B: \( \sqrt{1 – x^2} \)
C: \( x^2 – 1 \)
D: \( 1 – x^2 \)

Explanation: From the trigonometric identity sec²A – tan²A = 1, tan²A = sec²A – 1 = x² – 1. Therefore tan A = √(x² – 1).

Q15: A 10 meter long ladder is placed on the ground at a distance of 8 meters from a wall. What is the sine of the angle between the ladder and the wall?

A: \( \frac{4}{5} \)
B: \( \frac{3}{5} \)
C: \( \frac{5}{4} \)
D: \( \frac{5}{3} \)

Explanation: Let the length of the ladder AC = 10 meters, distance from the wall BC = 8 meters. In triangle ABC, angle A is the angle between the ladder and the wall. sin A = BC/AC = 8/10 = 4/5.

Quiz Results

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Class 10 Maths Chapter 8 Introduction to Trigonometry MCQs Quiz

Chapter 8, ‘Introduction to Trigonometry,’ is your first step into the world of trigonometry. In this chapter, you will learn how the ratios of the sides of a right-angled triangle are defined as Trigonometric Ratios like sin, cos, tan, cosec, sec, and cot. You will learn to calculate the values of these ratios for specific angles like 0°, 30°, 45°, 60°, and 90°. The chapter also covers crucial topics like Trigonometric Identities and the Trigonometric Ratios of Complementary Angles, which are foundational for the next chapter and the CBSE Class 10 Maths Quiz.

Conclusion

A strong grasp of trigonometry is essential for excelling in mathematics. Our Class 10 Maths Chapter 8 Introduction to Trigonometry MCQs Quiz is designed to help you master this important chapter. This quiz provides practice in remembering and applying the Trigonometry formulas for class 10 to various problems. By solving these objective questions, you can improve your speed and accuracy, which is highly beneficial for your Board Exam Preparation. Try this Free Online Trigonometry Quiz now and take your preparation to the next level!

FAQs on Trigonometry MCQs

1. Question: How many marks from the chapter Introduction to Trigonometry are asked in the board exam?
Answer: This chapter typically carries 8-10 marks in the CBSE board exam, including MCQs, short answer, and long answer questions.

2. Question: What are the most important topics in this chapter?
Answer: The most important topics are the Trigonometric Ratios, their value table (sin cos tan values table), Trigonometric Identities, and the ratios of complementary angles.

3. Question: Is this Trigonometry quiz based on the NCERT syllabus?
Answer: Yes, our Introduction to Trigonometry Class 10 quiz is fully based on the NCERT curriculum and the CBSE syllabus.

4. Question: How can I easily remember the values of sin, cos, and tan?
Answer: You can use a simple table or mnemonics to remember the values of trigonometric ratios for specific angles.

5. Question: What are trigonometric identities?
Answer: Trigonometric identities are equations that hold true for all values of the angles involved, such as sin²θ + cos²θ = 1. They are used to simplify and prove equations.

6. Question: Is this online quiz free?
Answer: Yes, this Free Online Trigonometry Quiz is absolutely free. You can take it anytime and anywhere for practice.

7. Question: How should I prepare this chapter for the board exam?
Answer: First, memorize all the Trigonometric Ratios and their values. Then, understand the identities and practice the examples from the NCERT book. Finally, test your knowledge with our Trigonometry Online Test.

8. Question: What are complementary angles?
Answer: Two angles are complementary if their sum is 90 degrees. For example, 30° and 60° are complementary angles.

9. Question: Does this quiz include proof-based questions?
Answer: This quiz is primarily MCQ-based, but these questions will strengthen your concepts to a level where you can easily solve proof-based questions.

10. Question: What is the benefit of taking this online quiz?
Answer: This quiz helps you improve time management, check the accuracy of your formulas, and understand the exam pattern, which boosts your confidence and leads to better performance.

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Introduction to Trigonometry MCQs Quiz

Quiz Results

Class 10 Maths Chapter 8 Introduction to Trigonometry MCQs Quiz

Conclusion

FAQs on Trigonometry MCQs

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