KTUYSBeta
Log inSign up

Cheat sheet · Class 12 · CBSE · Commerce Mathematics

Inverse Trigonometric Functions cheat sheet

The whole chapter on one page: key formulas, facts and the points to remember, for quick revision before a test.

CBSE Class 12 · Mathematics

Cheat sheet

Chapter 2Inverse Trigonometric Functions

Principal ranges: sin⁻¹ [−π/2, π/2], cos⁻¹ [0, π], tan⁻¹ (−π/2, π/2).

1. Domains & Principal Ranges

FunctionDomainRange
sin⁡−1x\sin^{-1}x[−1, 1][−π2,π2][-\tfrac\pi2, \tfrac\pi2]
cos⁡−1x\cos^{-1}x[−1, 1][0,π][0, \pi]
tan⁡−1x\tan^{-1}xℝ(−π2,π2)(-\tfrac\pi2, \tfrac\pi2)
cot⁡−1x\cot^{-1}xℝ(0,π)(0, \pi)
sec⁡−1x\sec^{-1}x|x| ≥ 1[0,π]−{π2}[0, \pi] - \{\tfrac\pi2\}
csc⁡−1x\csc^{-1}x|x| ≥ 1[−π2,π2]−{0}[-\tfrac\pi2, \tfrac\pi2] - \{0\}

2. Properties

sin⁡−1(−x)=−sin⁡−1x\sin^{-1}(-x) = -\sin^{-1}xcos⁡−1(−x)=π−cos⁡−1x\cos^{-1}(-x) = \pi - \cos^{-1}x
sin⁡−1x+cos⁡−1x=π2\sin^{-1}x + \cos^{-1}x = \dfrac\pi2
tan⁡−1x+cot⁡−1x=π2\tan^{-1}x + \cot^{-1}x = \dfrac\pi2

3. Key Points

  • Always answer in the principal range.
  • sin⁻¹x ≠ 1/sin x.
  • Graph of inverse: reflect in y = x.
  • sin⁻¹(sin x) = x only in the principal range.

Remember: Domain & range table | complementary identities

Inverse Trigonometric Functions: questions and notes

More Class 12 · CBSE · Commerce Mathematics cheat sheets

Practise Inverse Trigonometric Functions

Sign up free to practise the full chapter. Questions you get wrong come back until you've mastered them.

Start practising free

Free to start · No credit card needed