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Class 12

Inverse Trigonometric Functions — Course Quiz

Ten questions on principal values and properties of inverse trigonometric functions. Pick one answer for each.

10 questions, one mark each. 6 to pass. Suggested time: 20 minutes. Your answers are not recorded.

  1. The range (principal value branch) of tan⁡−1x\tan^{-1}x is
  2. The principal value of tan⁡−1(−1)\tan^{-1}(-1) is
  3. The principal value of csc⁡−1(−2)\csc^{-1}(-\sqrt{2}) is
  4. Find cos⁡−112+sin⁡−1(−32)\displaystyle \cos^{-1}\tfrac{1}{2} + \sin^{-1}\left(-\tfrac{\sqrt{3}}{2}\right).
  5. Find cos⁡−1(cos⁡5π4)\displaystyle \cos^{-1}\left(\cos\tfrac{5\pi}{4}\right).
  6. The domain of sin⁡−1(2x+1)\sin^{-1}(2x + 1) is
  7. cos⁡−1(−13)\displaystyle \cos^{-1}\left(-\tfrac{1}{3}\right) equals
  8. Find tan⁡−114+tan⁡−135\displaystyle \tan^{-1}\tfrac{1}{4} + \tan^{-1}\tfrac{3}{5}.
  9. Find cos⁡(tan⁡−134)\displaystyle \cos\left(\tan^{-1}\tfrac{3}{4}\right).
  10. Using the sum formula, the equation tan⁡−1x+tan⁡−12x=π4\displaystyle \tan^{-1}x + \tan^{-1}2x = \tfrac{\pi}{4} reduces to which equation in xx?
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