Mathematics
Introduction 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.
Practice questions
Which statement is correct about \(\sec^{-1}0\)?What is the horizontal limiting value of (\tan^{-1}x) when (x) is very large and positive?What is the horizontal limiting value of tan⁻¹x when x is very large and negative?What is the domain of the function (\sin^{-1}x)?What is the domain of \(\cos^{-1}x\)?What is the principal value range of \(\tan^{-1}x\)?What is the value of (\cos^{-1}1)?What is the principal value of (\tan^{-1}1)?What is (\tan(\tan^{-1}x)) equal to when (x\in\mathbb{R})?When can \(\sin^{-1}(\sin x)=x\) be directly true?When can \(\cos^{-1}(\cos x)=x\) be directly true?When can \(\tan^{-1}(\tan x)=x\) be directly true?What is the value of (\sin^{-1}x+\cos^{-1}x) when (x\in[-1,1])?If (\sin^{-1}x=\frac{\pi}{6}), what is the value of (x)?If (\cos^{-1}x=\frac{\pi}{3}), what is the value of (x)?If (\tan^{-1}x=\frac{\pi}{4}), what is the value of (x)?What is the domain of (\cot^{-1}x)?What is the usual principal value range of \(\cot^{-1}x\)?Which expression is not defined?What condition on x makes sin⁻¹x real?