Inverse Trigonometric Functions

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Questions and Answers

What is the range of the inverse sine function?

  • (-π/2, π/2)
  • [-1, 1]
  • [0, π]
  • [-π/2, π/2] (correct)

What is the notation for the inverse cosine function?

  • arccos(x) (correct)
  • tan^-1(x)
  • arcsin(x)
  • sin(x)

What is the domain of the inverse tangent function?

  • [-1, 1]
  • [0, π]
  • (-π/2, π/2)
  • ℝ (all real numbers) (correct)

What is the characteristic of the graph of y = arcsin(x)?

<p>It is symmetric about the origin (A)</p> Signup and view all the answers

What is the identity for arcsin(x) when x < 0?

<p>arcsin(x) = -arccos(√(1 - x^2)) (D)</p> Signup and view all the answers

What is the trigonometric identity for sin(arcsin(x))?

<p>sin(arcsin(x)) = x (D)</p> Signup and view all the answers

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Study Notes

Inverse Trigonometry

arcsin (sin^-1)

  • Also known as the inverse sine function
  • Defined as the angle whose sine is a given value
  • Notation: arcsin(x) or sin^-1(x)
  • Domain: [-1, 1]
  • Range: [-π/2, π/2]

arccos (cos^-1)

  • Also known as the inverse cosine function
  • Defined as the angle whose cosine is a given value
  • Notation: arccos(x) or cos^-1(x)
  • Domain: [-1, 1]
  • Range: [0, π]

arctan (tan^-1)

  • Also known as the inverse tangent function
  • Defined as the angle whose tangent is a given value
  • Notation: arctan(x) or tan^-1(x)
  • Domain: ℝ (all real numbers)
  • Range: (-π/2, π/2)

Inverse Sine Graph

  • The graph of y = arcsin(x) is symmetric about the origin
  • The graph has a horizontal asymptote at y = π/2 and a horizontal asymptote at y = -π/2
  • The graph is increasing on its entire domain

Trigonometric Identities

  • sin(arcsin(x)) = x
  • cos(arccos(x)) = x
  • tan(arctan(x)) = x
  • arcsin(x) = arccos(√(1 - x^2)) for x ≥ 0
  • arcsin(x) = -arccos(√(1 - x^2)) for x < 0

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