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Inverse Trigonometric Functions quiz

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  • What interval are the angles returned by the inverse cosine function restricted to?
    The angles returned by the inverse cosine function are restricted to the interval [0, π].
  • What values can be input into the inverse sine function?
    The input values for the inverse sine function must be between -1 and 1.
  • What is the output interval for the inverse sine function?
    The output angles for the inverse sine function are between -π/2 and π/2.
  • What is the output interval for the inverse tangent function?
    The output angles for the inverse tangent function are between -π/2 and π/2.
  • What is the inverse cosine of 1/2?
    The inverse cosine of 1/2 is π/3, since π/3 is within the interval [0, π].
  • What is the inverse sine of 1/2?
    The inverse sine of 1/2 is π/6, since π/6 is within the interval [-π/2, π/2].
  • What is the inverse sine of -√2/2?
    The inverse sine of -√2/2 is -π/4, since -π/4 is within the interval [-π/2, π/2].
  • What is the inverse tangent of √3?
    The inverse tangent of √3 is π/3, since π/3 is within the interval [-π/2, π/2].
  • What is the inverse tangent of -1?
    The inverse tangent of -1 is -π/4, since -π/4 is within the interval [-π/2, π/2].
  • How do you evaluate composite functions like sin(cos⁻¹(1/2))?
    Evaluate the inner function first (cos⁻¹(1/2) = π/3), then apply the outer function (sin(π/3) = √3/2).
  • What is the cosine of the inverse tangent of 0?
    The cosine of the inverse tangent of 0 is 1, since tan⁻¹(0) = 0 and cos(0) = 1.
  • What is the inverse cosine of the sine of π/3?
    The sine of π/3 is √3/2, and the inverse cosine of √3/2 is π/6.
  • Why can't you simply cancel inverse trig functions with their corresponding trig functions in composite expressions?
    You must consider the interval for which the inverse function is defined; simply canceling may give an incorrect answer.
  • What is the inverse cosine of the cosine of 11π/6?
    The cosine of 11π/6 is √3/2, and the inverse cosine of √3/2 is π/6, not 11π/6.
  • What happens if you try to evaluate the inverse sine of 2?
    The inverse sine of 2 is undefined because 2 is outside the interval [-1, 1] for valid input values.