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
What is the value of (\sin^{-1}1)?What is the principal value of \(\cot^{-1}0\)?Which of the following inverse trigonometric functions has all real numbers as its domain?If (y=\sin^{-1}x), what does it mean?If y = \cos^{-1}x, which relation is correct?If \(y=\tan^{-1}x\), which of the following is true?What happens when \(x=2\) is used in \(\sin^{-1}x\)?Which of the following statements is correct about \(\tan^{-1}5\)?What is the correct statement about \(\sec^{-1}\left(\frac{1}{2}\right)\)?What type of function is (\sin^{-1}x)?What is the correct meaning of the exponent (-1) in (\sin^{-1}x)?What is the value of \(\sin^{-1}x+\cos^{-1}x\) when \(x\in\left[-1,1\right]\)?What is the value of (\tan^{-1}x+\cot^{-1}x)?If \(\theta=\sin^{-1}\left(\frac{3}{5}\right)\), what is the value of \(sin\theta\)?If \(\theta=\cos^{-1}\left(\frac{4}{5}\right)\), what is the value of \(\cos\theta\)?If \(\theta=\tan^{-1}\left(\frac{5}{12}\right)\), what is the value of \(\tan\theta\)?If \(\theta=\tan^{-1}\left(\frac{8}{15}\right)\), what is the value of \(\cos\theta\)?How does cos⁻¹x behave on its domain [−1, 1]?Which statement is correct about \(\tan^{-1}x\)?How does \(\cot^{-1}x\) behave on its domain \(\mathbb{R}\)?