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Questions and Answers

What is the correct definition of the sine function based on the right triangle definition?

  • sin(θ) = adjacent / hypotenuse
  • sin(θ) = opposite / adjacent
  • sin(θ) = opposite / hypotenuse (correct)
  • sin(θ) = hypotenuse / opposite

    • Which of the following statements correctly represents the domain of the tangent function?

  • θ can be any angle except 90 degrees
  • θ cannot equal nπ, where n is any integer
  • θ can be any angle
  • θ cannot equal n + π, where n is any integer (correct)

    • What is the period of the function cos(ωθ)?

  • 2πω
  • 2π
  • ω (correct)
  • π

    • What does the cosecant function equal in terms of sine?

    <p>csc(θ) = hypotenuse / opposite</p> Signup and view all the answers

    Which of the following functions has the same periodicity as the sine function?

    <p>csc(θ)</p> Signup and view all the answers

    What is the relationship between secant and cosine?

    <p>sec(θ) = 1 / cos(θ)</p> Signup and view all the answers

    In terms of the unit circle, which coordinates correspond to the sine function?

    <p>(cos(θ), sin(θ))</p> Signup and view all the answers

    Which of the following is NOT defined for the cosecant function?

    <p>nπ where n is any integer</p> Signup and view all the answers

    Which of the following statements about the range of the sine function is true?

    <p>The sine function ranges from -1 to 1.</p> Signup and view all the answers

    Which identity correctly represents the relationship between tangent and cotangent?

    <p>tan(θ) = 1/cot(θ)</p> Signup and view all the answers

    Which of the following ranges is correct for the cosecant function?

    <p>csc(θ) ≥ 1 and csc(θ) ≤ −1</p> Signup and view all the answers

    What is the correct expression to define tan(θ) using sine and cosine?

    <p>tan(θ) = sin(θ)/cos(θ)</p> Signup and view all the answers

    The inverse function sin^(-1)(x) is defined for which domain?

    <p>−1 ≤ x ≤ 1</p> Signup and view all the answers

    What is the formula for the sine of a double angle?

    <p>sin(2θ) = 2sin(θ)cos(θ)</p> Signup and view all the answers

    Which of the following statements about the periodic properties of sine is correct?

    <p>sin(θ + 2π) = sin(θ)</p> Signup and view all the answers

    In which scenario is the cosecant function undefined?

    <p>When sin(θ) = 0</p> Signup and view all the answers

    What is the result of applying the Even/Odd formula to the cosine function?

    <p>cos(-θ) = cos(θ)</p> Signup and view all the answers

    What is the domain of the function tan^(-1)(x)?

    <p>−∞ &lt; x &lt; ∞</p> Signup and view all the answers

    Which identity accurately describes the relationship between the cosine and sine of complementary angles?

    <p>Both B and C are correct.</p> Signup and view all the answers

    Which of the following is not a Pythagorean identity?

    <p>tan²(θ) + 1 = cot²(θ)</p> Signup and view all the answers

    Which of the following is the definition of the cosecant function?

    <p>csc(θ) = 1/sin(θ)</p> Signup and view all the answers

    The formula for the secant function is derived from which basic function?

    <p>cos(θ)</p> Signup and view all the answers

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