In NCERT Class 12 Mathematics Chapter 2, titled Inverse Trigonometric Functions, students explore the inverse functions of trigonometric functions such as sine, cosine, tangent, cotangent, secant, and cosecant. The chapter explains how to determine the values of inverse trigonometric functions, focusing on their domains and ranges. The principal values of these inverse functions are crucial for solving trigonometric equations and proving identities. Students also learn to apply these functions in various real-life scenarios and mathematical problems.
This article provides a comprehensive resource for exam preparation. It includes sample MCQs and subjective questions for CBSE and CUET, alongside downloadable PDFs of Class 12 Mathematics Chapter 2 MCQs and previous year questions for detailed practice of NCERT Class 12 Inverse Trigonometric Functions.
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NCERT Class 12 Mathematics Chapters
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Class 12 Mathematics Chapter 2 MCQs
This question bank includes previous years' CUET and CBSE MCQs, along with questions curated by subject experts. Below are 5 sample multiple-choice questions (MCQs) for Class 12 Mathematics Chapter 2: Inverse Trigonometric Functions. For the full set of 50 questions, download the PDF using the link provided below.
- The domain of the function \( f(x) = \sin^{-1}(x) \) is:
(a) [-1,1]
(b) (-∞,∞)
(c) [0,1]
(d) [-∞,∞]
- The range of the function \( \cos^{-1}(x) \) is:
(a) [0,π]
(b) [-1,1]
(c) [-π,π]
(d) [0,2π]
- If \( y = \tan^{-1}(x) \), then:
(a) \( y = \frac{x}{1 + x^2} \)
(b) \( y = \sin^{-1}(x) \)
(c) \( y = \tan^{-1}(x) \)
(d) \( y = \cos^{-1}(x) \)
- The principal value of \( \sin^{-1}(\frac{1}{2}) \) is:
(a) \( \frac{\pi}{6} \)
(b) \( \frac{\pi}{4} \)
(c) \( \frac{\pi}{3} \)
(d) \( \frac{\pi}{2} \)
- If \( \tan^{-1}(x) + \cot^{-1}(x) = \frac{\pi}{2} \), then the value of \( x \) is:
(a) 0
(b) 1
(c) \( \sqrt{2} \)
(d) -1
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Class 12 Mathematics Chapter 2 Subjective Questions Without Solutions
This question bank includes previous years' CBSE subjective questions (2 marks and above) without solutions, along with expert-curated questions. Below are 5 sample subjective questions for Class 12 Mathematics Chapter 2: Inverse Trigonometric Functions. To access all questions, download the PDF from the link provided below.
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1.
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Draw the graph of cos−1𝑥, where 𝑥 ∈ [−1, 0]. Also, write its range.
(CBSE 2023, 2M)
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2.
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Draw the graph of f(x) = sin -1 x, x ∈ . Also, write range of f(x). (CBSE 2023, 2M)
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3.
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Find the domain of y = sin-1 (x2 - 4).
(CBSE 2023, 2M)
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4.
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Write the domain and range (principle value branch) of the following functions :
f(x) = tan-1 x
(CBSE 2023, 2M)
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5.
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Draw the graph of the principal branch of the function f(x) = cos-1 x.
(CBSE 2023, 2M)
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NCERT Mathematics Topics
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Chapter Name
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Sub Topics
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Chapter 2: Inverse Trigonometric Functions
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2.1 Introduction
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2.2 Definition of Inverse Trigonometric Functions
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2.3 Range and Domain of Inverse Trigonometric Functions
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2.4 Principal Values of Inverse Trigonometric Functions
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2.5 Properties of Inverse Trigonometric Functions
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2.6 Solving Trigonometric Equations using Inverse Functions
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2.7 Graphs of Inverse Trigonometric Functions
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Review of NCERT Class 12 Mathematics Chapter 2
NCERT Class 12 Mathematics Chapter 2, Inverse Trigonometric Functions, is an essential chapter for understanding the concepts and properties of inverse trigonometric functions. It lays the foundation for solving complex trigonometric equations and performing integrations in calculus. The chapter also helps students understand the principal values and range of inverse trigonometric functions, which are crucial for higher studies in mathematics.
By mastering the techniques in this chapter, students will be well-equipped to solve a variety of problems, and it will enhance their preparation for exams like CBSE, CUET, and other competitive exams.