Mathematics
Inverse Trigonometric Functions
प्रतिलोम त्रिकोणमितीय फलन
In Class 12 Mathematics, the chapter Inverse Trigonometric Functions introduces inverse relations for trigonometric functions and explains how restricted domains create single-valued inverses. Students study domain, range, and principal value branches of inverse sine, cosine, tangent, cotangent, secant, and cosecant functions. The chapter also develops their graphs and key properties, helping learners interpret values and solve expressions involving inverse trigonometric functions.
1Introduction to inverse trigonometric functions
प्रतिलोम त्रिकोणमितीय फलनों का परिचय
This Class 12 Mathematics topic introduces inverse trigonometric functions as the functions that reverse the action of sine, cosine, and tangent on suitably restricted domains. Students learn the meaning of sin⁻¹x, cos⁻¹x, and tan⁻¹x, along with their principal values, domains, and ranges. The topic also develops understanding of how these functions are represented, how their restrictions make them well-defined, and how to interpret basic relationships and expressions within the chapter on Inverse Trigonometric Functions.
101 questionsDomain and range
परिभाषा-क्षेत्र और परास
In this Class 12 Mathematics topic from the chapter Inverse Trigonometric Functions, students learn to identify the domain—the set of permitted input values—and the range—the resulting output values—of functions and inverse trigonometric functions. The topic explains how restrictions on sine, cosine and tangent functions make inverse functions well-defined, how principal value ranges are selected, and how domains and ranges can be interpreted from formulas, graphs and function relationships.
24 questionsPrincipal value branch
प्रधान मान शाखा
In this Class 12 Mathematics topic from Inverse Trigonometric Functions, students learn why trigonometric functions must be restricted to suitable domains to have well-defined inverses. The topic explains the principal value branch, standard ranges of sin⁻¹x, cos⁻¹x, tan⁻¹x and related functions, and how these ranges determine the unique value returned by an inverse function. Students also practise interpreting graphs, selecting correct branches, and applying principal-value conventions while simplifying expressions and solving problems.
70 questionsGraphs of inverse trigonometric functions
प्रतिलोम त्रिकोणमितीय फलनों के ग्राफ
In this Class 12 Mathematics topic from the chapter “Inverse Trigonometric Functions,” students learn how to sketch and interpret the graphs of sin⁻¹x, cos⁻¹x, tan⁻¹x and related functions. The topic connects each graph with its parent trigonometric function through reflection and restriction of domain, while emphasizing principal values, domains, ranges, intercepts, symmetry and key points. Students also examine how transformations affect these graphs and use them to understand inverse-function relationships.
4 questionsProperties of inverse trigonometric functions
प्रतिलोम त्रिकोणमितीय फलनों के गुणधर्म
In Class 12 Mathematics, this topic from the chapter “Inverse Trigonometric Functions” helps students understand the principal values, domains, and ranges of sin⁻¹x, cos⁻¹x, tan⁻¹x and related functions. It covers standard identities, relationships between inverse trigonometric functions, and the conditions needed to simplify expressions correctly. Students also learn to evaluate compositions and use these properties to solve equations and verify results without confusing restricted angles or function branches.
51 questions