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Indian Navy INET Calculus — practice questions

Explore 27 free Calculus questions in Indian Navy INET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Calculus questions and exercises with answers

Showing questions 1–27 of 27.

The double angle formula sin 2A equals:Read 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

The double angle formula sin 2A equals:

  1. $\sin A + \cos A$ (incorrect sum)
  2. $2 \sin A \cos A$ (the correct formula)
  3. $\sin^2 A - \cos^2 A$ (resembles cos 2A)
  4. $2 \sin^2 A$ (only partial)
Show answer and solution

Correct answer: B. $2 \sin A \cos A$ (the correct formula)

sin 2A = 2 sin A cos A. Comes from sin(A+A) = sin A cos A + cos A sin A. cos 2A has multiple equivalent forms: cos²A − sin²A = 2cos²A − 1 = 1 − 2sin²A.

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Sort each inverse function into its domain

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Items
  1. Item
    sin⁻¹ x
    Category
    [−1, 1]
  2. Item
    cos⁻¹ x
    Category
    [−1, 1]
  3. Item
    cosec⁻¹ x
    Category
    R − (−1, 1)
  4. Item
    sec⁻¹ x
    Category
    R − (−1, 1)
  5. Item
    tan⁻¹ x
    Category
    R
  6. Item
    cot⁻¹ x
    Category
    R
Categories
  1. Item
    [−1, 1]
  2. Item
    R − (−1, 1)
  3. Item
    R
Only sin⁻¹ and cos⁻¹ accept every value from −1 to 1. cosec⁻¹ and sec⁻¹ need |x| ≥ 1, so the open middle is cut out. tan⁻¹ and cot⁻¹ accept any real number. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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Tap every function whose domain is [−1, 1]

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Questions
  1. Items
    1. Text
      sin⁻¹ x
      Matches the category
      Yes
    2. Text
      cos⁻¹ x
      Matches the category
      Yes
    3. Text
      tan⁻¹ x
      Matches the category
      No
    4. Text
      sec⁻¹ x
      Matches the category
      No
    5. Text
      cot⁻¹ x
      Matches the category
      No
    6. Text
      cosec⁻¹ x
      Matches the category
      No
    Category
    Domain is [−1, 1]
  2. Items
    1. Text
      tan⁻¹ x
      Matches the category
      Yes
    2. Text
      cot⁻¹ x
      Matches the category
      Yes
    3. Text
      sin⁻¹ x
      Matches the category
      No
    4. Text
      cosec⁻¹ x
      Matches the category
      No
    5. Text
      sec⁻¹ x
      Matches the category
      No
    6. Text
      cos⁻¹ x
      Matches the category
      No
    Category
    Domain is all of R
  3. Items
    1. Text
      cosec⁻¹ x
      Matches the category
      Yes
    2. Text
      sec⁻¹ x
      Matches the category
      Yes
    3. Text
      sin⁻¹ x
      Matches the category
      No
    4. Text
      cos⁻¹ x
      Matches the category
      No
    5. Text
      tan⁻¹ x
      Matches the category
      No
    6. Text
      cot⁻¹ x
      Matches the category
      No
    Category
    Domain leaves out the open interval (−1, 1)
sin⁻¹ and cos⁻¹ are the two inverses defined exactly on [−1, 1], because sine and cosine themselves only ever output values in that interval. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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