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Indian Navy MR Inverse Trigonometric Functions — practice questions

Explore 30 free Inverse Trigonometric Functions questions in Indian Navy MR Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Inverse Trigonometric Functions questions and exercises with answers

Showing questions 1–30 of 30.

If $\tan^{-1}\left(\dfrac{1}{2}\right) + \tan^{-1}\left(\dfrac{1}{3}\right) = ?$Read the answer and worked solution →Range of arcsin(x) (principal value):Read the answer and worked solution →d/dx arcsin(x) =Read the answer and worked solution →$\displaystyle \sum_{n=1}^{\infty} \tan^{-1}\left(\frac{1}{n^2 + n + 1}\right)$ equalsRead the answer and worked solution →Sort each inverse function into its domainRead the answer and worked solution →Tap every function whose domain is [−1, 1]Read the answer and worked solution →Match each inverse function to its domainRead the answer and worked solution →Match each inverse function to its principal value branchRead the answer and worked solution →Flip and pair: function with its principal rangeRead the answer and worked solution →Which principal ranges sit around zero, and which run 0 to π?Read the answer and worked solution →Tap every function whose principal range has a point removedRead the answer and worked solution →Name the principal value branchRead the answer and worked solution →Domain checkRead the answer and worked solution →Put the reasoning in order: why an inverse needs a restricted domainRead the answer and worked solution →True or false: existence of inversesRead the answer and worked solution →True or false: reading the tableRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Complete the summary tableRead the answer and worked solution →Complete the rule about restricting a domainRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Principal values worked in the chapterRead the answer and worked solution →Order the steps for finding a principal valueRead the answer and worked solution →True or false: principal valuesRead the answer and worked solution →Match each identity to the condition it needsRead the answer and worked solution →Assertion and reason: identitiesRead the answer and worked solution →Match each mathematician to the year your syllabus givesRead the answer and worked solution →Trace how trigonometry travelledRead the answer and worked solution →True or false: the historical noteRead the answer and worked solution →

Worked practice questions

If $\tan^{-1}\left(\dfrac{1}{2}\right) + \tan^{-1}\left(\dfrac{1}{3}\right) = ?$

  1. $\dfrac{\pi}{3}$
  2. $\dfrac{\pi}{2}$
  3. $\dfrac{\pi}{6}$
  4. $\dfrac{\pi}{4}$
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Correct answer: D. $\dfrac{\pi}{4}$

Use the identity $\tan^{-1}(a) + \tan^{-1}(b) = \tan^{-1}\left(\dfrac{a + b}{1 - ab}\right)$, valid when $ab < 1$. With $a = 1/2$, $b = 1/3$: $ab = 1/6 < 1$, so the identity applies cleanly. $\dfrac{a + b}{1 - ab} = \dfrac{1/2 + 1/3}{1 - 1/6} = \dfrac{5/6}{5/6} = 1$. So the sum equals $\tan^{-1}(1) = \dfrac{\pi}{4}$.

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Range of arcsin(x) (principal value):

  1. [-π/2, π/2]
  2. [0, π]
  3. [0, 2π]
  4. All reals
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Correct answer: A. [-π/2, π/2]

sin⁻¹(x) defined for x ∈ [-1, 1]. **Principal range:** [-π/2, π/2]. Restriction makes inverse well-defined.

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d/dx arcsin(x) =

  1. 1/sqrt(1+x²)
  2. -1/sqrt(1-x²)
  3. 1/sqrt(1-x²) (for |x| < 1)
  4. 1/x
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Correct answer: C. 1/sqrt(1-x²) (for |x| < 1)

Derivative of sin⁻¹(x) = 1/sqrt(1-x²) for |x| < 1. (And d/dx cos⁻¹ = -1/sqrt(1-x²).)

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