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AP Calculus AB Unit 1A2: Trigonometric Functions & Inverse Trig — practice questions — page 2

Explore 94 free Unit 1A2: Trigonometric Functions & Inverse Trig questions in AP Calculus AB Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Unit 1A2: Trigonometric Functions & Inverse Trig questions and exercises with answers

Showing questions 31–60 of 94.

Equivalence relation requires:Read the answer and worked solution →For sets A, B: A × B = B × A iff:Read the answer and worked solution →|A| = 5, |B| = 3. Number of relations from A to B:Read the answer and worked solution →For f: A → B and g: B → C, (g ∘ f)⁻¹ =Read the answer and worked solution →Function f(x) = (x-1)/(x+2) on R - {-2}. f is bijection from R - {-2} to R - {?}:Read the answer and worked solution →Equivalence classes of 'congruent mod 3' on Z:Read the answer and worked solution →Number of one-one and onto (bijective) functions from {1,2,3} to {1,2,3}:Read the answer and worked solution →For function f(x) = ax + b (a ≠ 0), inverse is:Read the answer and worked solution →For f: R → R, f(x) = x³, f is:Read the answer and worked solution →Inverse image f⁻¹(B) under f: X → Y for B ⊆ Y:Read the answer and worked solution →Range of f(x) = sin(x) from R to R:Read the answer and worked solution →Distributive law: A ∩ (B ∪ C) =Read the answer and worked solution →A relation from A to B is:Read the answer and worked solution →Empty set has cardinality:Read the answer and worked solution →A set is:Read the answer and worked solution →Domain of relation:Read the answer and worked solution →Identity function I: A → A is:Read the answer and worked solution →Universal set:Read the answer and worked solution →Function f: A → B is onto (surjective) if:Read the answer and worked solution →Power set of {1, 2, 3} has:Read the answer and worked solution →n(A ∪ B) =Read the answer and worked solution →De Morgan's law: (A ∪ B)' =Read the answer and worked solution →Cartesian product A × B has cardinality:Read the answer and worked solution →Number of functions from A (|A| = n) to B (|B| = m):Read the answer and worked solution →Inverse of function f exists if and only if f is:Read the answer and worked solution →Composition of functions (g ∘ f)(x) =Read the answer and worked solution →If A = {1, 2, 3, 4, 5}, B = {3, 4, 5, 6, 7}, find A ∩ B:Read the answer and worked solution →Number of subsets of {1, 2, 3, 4, 5} with exactly 3 elements:Read the answer and worked solution →For 3 sets A, B, C: n(A ∪ B ∪ C) =Read the answer and worked solution →Maximum value of sin(2 arctan(x)) over real x:Read the answer and worked solution →

Worked practice questions

Equivalence relation requires:

  1. Just reflexive
  2. REFLEXIVE + SYMMETRIC + TRANSITIVE
  3. Just transitive
  4. Anti-symmetric
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Correct answer: B. REFLEXIVE + SYMMETRIC + TRANSITIVE

**Equivalence relation:** aRa (reflexive), aRb ⇒ bRa (symmetric), aRb ∧ bRc ⇒ aRc (transitive). Partitions set into disjoint equivalence classes. e.g., 'congruence mod n', 'same age'.

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For sets A, B: A × B = B × A iff:

  1. Same cardinality
  2. Never
  3. A = B (or one of them empty)
  4. Always
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Correct answer: C. A = B (or one of them empty)

A × B and B × A consist of ordered pairs. A × B = B × A iff every (a, b) in A × B also belongs to B × A. Requires A = B (or both empty). **Hence Cartesian product is generally NOT commutative.**

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|A| = 5, |B| = 3. Number of relations from A to B:

  1. 125
  2. 2^15 = 32768
  3. 8
  4. 15
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Correct answer: B. 2^15 = 32768

2^(|A| × |B|) = 2^15 = 32768. Versus number of functions: 3^5 = 243. So relations vastly more than functions.

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More Mathematics topics

Unit 3B: Implicit Differentiation and Inverse FunctionsUnit 3A: Chain Rule and Composite FunctionsUnit 1A3: Function Composition and InversesUnit 1A1: Relations, Functions and GraphsUnit 2: Differentiation and Fundamental Derivative RulesUnit 6A: Indefinite Integrals & Fundamental TheoremUnit 1B3: Asymptotic Behavior and Infinite LimitsUnit 1B1: Limit Concepts and Graphical Limits