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OJEE Inverse Trigonometric Functions — practice questions — page 3

Explore 76 free Inverse Trigonometric Functions questions in OJEE 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 61–76 of 76.

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

True or false: existence of inverses

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Questions
  1. Statement is true
    Yes
    Statement
    A function has an inverse only when it is one-one and onto.
  2. Statement is true
    No
    Statement
    sin x is one-one over all of R, so sin⁻¹ needs no restriction.
  3. Statement is true
    Yes
    Statement
    Restricting sine to [−π/2, π/2] makes it one-one with range [−1, 1].
  4. Statement is true
    No
    Statement
    sin⁻¹ x means the same thing as (sin x)⁻¹.
  5. Statement is true
    Yes
    Statement
    (sin x)⁻¹ is 1/sin x, which is cosec x.
  6. Statement is true
    No
    Statement
    cos⁻¹ is defined for every real number.
The whole chapter rests on these. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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True or false: reading the table

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Questions
  1. Statement is true
    Yes
    Statement
    The principal range of cos⁻¹ is [0, π].
  2. Statement is true
    No
    Statement
    The principal range of tan⁻¹ is a closed interval.
  3. Statement is true
    Yes
    Statement
    cot⁻¹ has domain R and principal range (0, π).
  4. Statement is true
    Yes
    Statement
    sec⁻¹ has π/2 removed from its principal range.
  5. Statement is true
    No
    Statement
    cosec⁻¹ has π/2 removed from its principal range.
  6. Statement is true
    Yes
    Statement
    cosec⁻¹ and sec⁻¹ share the domain R − (−1, 1).
Each statement is a row of the summary table, stated straight or bent. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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Spot the one that does not belong

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Questions
  1. Items
    1. sin⁻¹ x
    2. cos⁻¹ x
    3. tan⁻¹ x
    Odd item
    tan⁻¹ x
  2. Items
    1. sec⁻¹ x
    2. tan⁻¹ x
    3. cot⁻¹ x
    Odd item
    sec⁻¹ x
  3. Items
    1. [−π/2, π/2]
    2. [0, π]
    3. (−π/2, π/2)
    Odd item
    [0, π]
  4. Items
    1. cosec⁻¹ x
    2. sec⁻¹ x
    3. cos⁻¹ x
    Odd item
    cos⁻¹ x
  5. Items
    1. (0, π)
    2. [−1, 1]
    3. R − (−1, 1)
    Odd item
    (0, π)
Each group is built on a single row or column of the summary table. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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