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Mathematics

Principal value branch

In this Class 12 Mathematics topic from Inverse Trigonometric Functions, students learn why trigonometric functions must be restricted to suitable domains to have well-defined inverses. The topic explains the principal value branch, standard ranges of sin⁻¹x, cos⁻¹x, tan⁻¹x and related functions, and how these ranges determine the unique value returned by an inverse function. Students also practise interpreting graphs, selecting correct branches, and applying principal-value conventions while simplifying expressions and solving problems.

Medium · Level 2 · 2 questions

Practice questions

01What is the value of \(\cos\left(\sin^{-1}\left(-\frac{5}{13}\right)\right)\)?

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Answer and explanation

02Which of the following inverse trigonometric functions has the principal-value range \([0,\pi]\)?

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Answer and explanation

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