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AP Calculus AB Unit 1A2: Trigonometric Functions & Inverse Trig — practice questions — page 4

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 91–94 of 94.

If $(x+1,\,y-2)=(3,\,1)$, then $(x,y)$ equals:Read the answer and worked solution →The domain of $f(x)=\sqrt{4-x^2}$ is:Read the answer and worked solution →A relation $f$ from $A$ to $B$ is a function if every element of $A$ has:Read the answer and worked solution →In a right triangle, for an acute angle θ, sin θ is defined as:Read the answer and worked solution →

Worked practice questions

If $(x+1,\,y-2)=(3,\,1)$, then $(x,y)$ equals:

  1. $(3,1)$
  2. $(4,-1)$
  3. $(2,-1)$
  4. $(2,3)$
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Correct answer: D. $(2,3)$

Equate components: x+1=3 ⟹ x=2; y−2=1 ⟹ y=3.

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The domain of $f(x)=\sqrt{4-x^2}$ is:

  1. $[0,2]$
  2. $(-2,2)$
  3. $[-2,2]$
  4. $\mathbb{R}$
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Correct answer: C. $[-2,2]$

Need 4−x² ≥ 0 ⟹ x² ≤ 4 ⟹ −2 ≤ x ≤ 2, i.e. [−2, 2].

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A relation $f$ from $A$ to $B$ is a function if every element of $A$ has:

  1. no image in B
  2. exactly one image in $B$
  3. an image equal to itself
  4. at least two images in B
Show answer and solution

Correct answer: B. exactly one image in $B$

A function assigns each element of the domain exactly one image in the codomain.

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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