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Indian Navy AA (Artificer Apprentice) Inverse Trigonometric Functions — practice questions

Explore 31 free Inverse Trigonometric Functions questions in Indian Navy AA (Artificer Apprentice) 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 31.

If $\tan^{-1}\left(\dfrac{1}{2}\right) + \tan^{-1}\left(\dfrac{1}{3}\right) = ?$Read the answer and worked solution →arctan(x) + arctan(1/x) (for x > 0) =Read the answer and worked solution →Value of arccos(-1):Read the answer and worked solution →Value of cos(arcsin(3/5)):Read the answer and worked solution →$\tan^{-1}\left(\tfrac{1}{2}\right) + \tan^{-1}\left(\tfrac{1}{3}\right)$ 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 →

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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arctan(x) + arctan(1/x) (for x > 0) =

  1. π
  2. 0
  3. Depends on x
  4. π/2
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Correct answer: D. π/2

For x > 0: tan⁻¹(x) + tan⁻¹(1/x) = π/2. For x < 0: -π/2. Cotangent of arctan(x) is 1/x, so the two angles are complementary.

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Value of arccos(-1):

  1. -π
  2. π/2
  3. 0
  4. π
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Correct answer: D. π

cos(π) = -1, so arccos(-1) = π. (Principal range [0, π].)

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