Domain and Range of Trig Functions Flashcards
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Questions and Answers

What is the domain of Sine and Cosine?

Both are the set of all real numbers.

What is the range of Sine and Cosine?

[-1,1]

What is the domain of Tangent?

Set of all real numbers, except odd multiples of π/2.

What is the range of Tangent?

<p>{y | -∞ &lt; y &lt; ∞}</p> Signup and view all the answers

What is the domain of Secant?

<p>Set of all real numbers, except odd multiples of π/2.</p> Signup and view all the answers

What is the range of Secant?

<p>{y | y ≤ -1 or y ≥ 1}</p> Signup and view all the answers

What is the domain of Cotangent?

<p>Set of all real numbers, except integer multiples of π.</p> Signup and view all the answers

What is the range of Cotangent?

<p>{y | -∞ &lt; y &lt; ∞}</p> Signup and view all the answers

What is the domain of Cosecant?

<p>Set of all real numbers, except integer multiples of π.</p> Signup and view all the answers

What is the range of Cosecant?

<p>{y | -1 ≤ y ≤ 1}</p> Signup and view all the answers

Study Notes

Domain and Range of Trigonometric Functions

  • Domain of Sine and Cosine

    • Defined as all real numbers
    • Expressed in interval notation: (-∞, ∞)

  • Range of Sine and Cosine

    • Values limited to the interval: [-1, 1]

  • Domain of Tangent

    • All real numbers except odd multiples of π/2 (90°)
    • Set notation representation: {Θ | Θ ≠ (2n-1)π/2, n ∈ Z}

  • Range of Tangent

    • Includes all real numbers
    • Expressed in interval notation: (-∞, ∞)

  • Domain of Secant

    • Like tangent, the domain consists of all real numbers except odd multiples of π/2 (90°)
    • Set notation: {Θ | Θ ≠ (2n-1)π/2, n ∈ Z}

  • Range of Secant

    • Values found in two intervals: y ≤ -1 or y ≥ 1
    • Interval notation: (-∞, -1] U [1, ∞)

  • Domain of Cotangent

    • Contains all real numbers except integer multiples of π (180°)
    • Set notation: {Θ | Θ ≠ nπ, n ∈ Z}

  • Range of Cotangent

    • All real numbers are included
    • Interval representation: (-∞, ∞)

  • Domain of Cosecant

    • Comprises all real numbers except integer multiples of π (180°)
    • Set notation is: {Θ | Θ ≠ nπ, n ∈ Z}

  • Range of Cosecant

    • Includes values y such that -1 ≤ y ≤ 1
    • Interval notation: (-∞, -1] U [1, ∞)

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Test your knowledge on the domain and range of trigonometric functions with these flashcards. This quiz covers key concepts essential for understanding sine, cosine, and tangent functions. Review the definitions and interval notations to master the subject.

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