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Class 12MathematicsInverse Trigonometric FunctionsPrincipal value branchEasy
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What is \(cos^{-1}\left(-x\right)\) equal to when \(x\in\left[-1,1\right]\)?

Answer and explanation

Correct answer: \(\pi-\cos^{-1}x\)

The relation \(cos^{-1}\left(-x\right)=\pi-\cos^{-1}x\) is correct because of principal values. Do not treat it as an odd function.

Related tags

Inverse Trigonometric FunctionsPrincipal ValueArccosPrincipal Value BranchMathematicsClass 12 Mcq
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10 more MCQs
  1. 1What is the principal value range of \(\sin^{-1}x\)?
  2. 2What is the principal value range of \(\cos^{-1}x\)?
  3. 3Which is the principal value range of \(\tan^{-1}x\)?
  4. 4What is the principal value range of \(\cot^{-1}x\)?
  5. 5What is the value of \(\sin^{-1}0\)?
  6. 6What is the value of \(\sin^{-1}\left(-1\right)\)?
  7. 7Find the value of \(\cos^{-1}1\).
  8. 8Find the principal value of \(\cos^{-1}(1)\).
  9. 9What is the value of \(\cos^{-1}(-1)\)?
  10. 10What is the value of \(\tan^{-1}0\)?
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