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CG PET Class12 Relations Basics — practice questions — page 3

Explore 101 free Class12 Relations Basics questions in CG PET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Class12 Relations Basics questions and exercises with answers

Showing questions 61–90 of 101.

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 →Complete the arc length relationRead the answer and worked solution →Match each identity to its nameRead the answer and worked solution →The Pythagorean identitiesRead the answer and worked solution →Odd function or even function?Read the answer and worked solution →Complete the degree and radian conversionRead the answer and worked solution →True or false: identities and parityRead the answer and worked solution →Match each sum or difference formula to its resultRead the answer and worked solution →Signs in the expansionRead the answer and worked solution →Which formula does this belong to?Read the answer and worked solution →True or false: periodicityRead the answer and worked solution →Complete the complementary angle rulesRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →Order the steps: convert degrees to radiansRead the answer and worked solution →Flip and pair: identity with its valueRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Tap every correct identityRead the answer and worked solution →Radians and degreesRead the answer and worked solution →True or false: reading the identitiesRead the answer and worked solution →Positive or negative angleRead the answer and worked solution →Which ratios are positiveRead the answer and worked solution →Type the trig functionRead the answer and worked solution →

Worked practice questions

Order the steps for finding a principal value

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Steps
  1. Let y be the inverse value you are asked for
  2. Rewrite it as the direct trigonometric equation
  3. Find an angle that satisfies that equation
  4. Check the angle lies inside the principal value branch
  5. If it does not, shift to the equivalent angle that does
This is the method your syllabus uses in Examples 1 and 2: name the value, convert to the direct function, find the angle then check it lies in the principal branch. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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True or false: principal values

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Questions
  1. Statement is true
    Yes
    Statement
    A principal value must lie inside the principal value branch.
  2. Statement is true
    Yes
    Statement
    sin⁻¹(1/√2) = π/4.
  3. Statement is true
    Yes
    Statement
    cot⁻¹(−1/√3) = 2π/3.
  4. Statement is true
    No
    Statement
    If no branch is stated, you may pick any branch you like.
  5. Statement is true
    Yes
    Statement
    When no branch is mentioned, the principal branch is meant.
Tests the one habit that decides these questions, which is checking the branch. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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Match each identity to the condition it needs

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Matching pairs
  1. Left
    sin (sin⁻¹ x) = x
    Right
    holds for x in [−1, 1]
  2. Left
    sin⁻¹ (sin x) = x
    Right
    holds for x in [−π/2, π/2]
  3. Left
    y = sin⁻¹ x
    Right
    means x = sin y
  4. Left
    (sin x)⁻¹
    Right
    means 1/sin x, i.e. cosec x
Your syllabus states both identities together with the interval each one holds on quoting one without its condition is the usual slip. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.

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