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AP Intermediate 2nd Year Relations, Functions & Inverse Trigonometry — practice questions — page 3

Explore 92 free Relations, Functions & Inverse Trigonometry questions in AP Intermediate 2nd Year Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Relations, Functions & Inverse Trigonometry questions and exercises with answers

Showing questions 61–90 of 92.

Tap every function whose domain is [−1, 1]Read the answer and worked solution →Flip and pair: function with its principal rangeRead 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 →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 →Two are true, one is notRead the answer and worked solution →Assertion and reasonRead 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 →Three of these are wrong. Find the one that holds.Read the answer and worked solution →For a binomial distribution B(n, p), the MEAN and VARIANCE are:Read the answer and worked solution →True or false: reading the tableRead the answer and worked solution →In a binomial distribution B(n=10, p=0.5), the probability of EXACTLY 6 successes is:Read the answer and worked solution →The value of $\cos^{-1}(-1)$ is:Read the answer and worked solution →For $x = -2$, the value of $\tan^{-1}\left(\dfrac{2x}{1-x^2}\right)$ equalsRead the answer and worked solution →The domain of the function $f(x) = \sin^{-1}(x)$ isRead the answer and worked solution →For every $x \in [-1, 1]$, the value of $\sin^{-1}(x) + \cos^{-1}(x)$ isRead the answer and worked solution →$\cos^{-1}\left(\cos\tfrac{7\pi}{6}\right)$ equalsRead the answer and worked solution →The value of $\sin(\tan^{-1}(3/4))$ is:Read the answer and worked solution →The principal value of $\tan^{-1}(1)$ isRead the answer and worked solution →Assertion and reason: identitiesRead the answer and worked solution →The range of $\cos^{-1}(x)$ isRead the answer and worked solution →Trace how trigonometry travelledRead the answer and worked solution →Match each inverse function to its principal value branchRead the answer and worked solution →Domain checkRead the answer and worked solution →True or false: principal valuesRead the answer and worked solution →True or false: the historical noteRead 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 →All real $x$ satisfying $\sin^{-1}(x) + \sin^{-1}(1-x) = \cos^{-1}(x)$ areRead the answer and worked solution →

Worked practice questions

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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Flip and pair: function with its principal range

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Matching pairs
  1. A
    sin⁻¹ x
    B
    [−π/2, π/2]
  2. A
    cos⁻¹ x
    B
    [0, π]
  3. A
    cosec⁻¹ x
    B
    [−π/2, π/2] − {0}
  4. A
    sec⁻¹ x
    B
    [0, π] − {π/2}
  5. A
    tan⁻¹ x
    B
    (−π/2, π/2)
  6. A
    cot⁻¹ x
    B
    (0, π)
Learning the six ranges as pairs is the fastest route through most exam questions on this chapter. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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Tap every function whose principal range has a point removed

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Questions
  1. Items
    1. Text
      cosec⁻¹ x removes 0
      Matches the category
      Yes
    2. Text
      sec⁻¹ x removes π/2
      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
    Principal range has a point cut out
  2. Items
    1. Text
      tan⁻¹ x (−π/2, π/2)
      Matches the category
      Yes
    2. Text
      cot⁻¹ x (0, π)
      Matches the category
      Yes
    3. Text
      sin⁻¹ x [−π/2, π/2]
      Matches the category
      No
    4. Text
      cos⁻¹ x [0, π]
      Matches the category
      No
    Category
    Principal range is an OPEN interval
cosec⁻¹ drops 0 and sec⁻¹ drops π/2, because cosec and sec are undefined there. The other four ranges are unbroken. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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