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Inverse Sine, Cosine, & Tangent quiz

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  • What does an inverse trig function do in relation to its corresponding trig function?
    An inverse trig function undoes its corresponding trig function, allowing you to find the angle from a given value.
  • What is the domain (input values) for the inverse cosine function?
    The domain for inverse cosine is all values between -1 and 1.
  • What is the range (output angles) for the inverse cosine function?
    The range for inverse cosine is all angles between 0 and π.
  • How do you evaluate an expression like inverse cosine of 1/2?
    You find the angle on the unit circle whose cosine value is 1/2, which is π/3.
  • Why is 5π/3 not the solution to inverse cosine of 1/2?
    Because 5π/3 is not within the specified range of 0 to π for inverse cosine.
  • What is the domain for the inverse sine function?
    The domain for inverse sine is all values between -1 and 1.
  • What is the range for the inverse sine function?
    The range for inverse sine is all angles between -π/2 and π/2.
  • What is the value of inverse sine of 1/2?
    The value is π/6, since sine of π/6 equals 1/2 and π/6 is within the correct interval.
  • Why is 5π/6 not the solution to inverse sine of 1/2?
    Because 5π/6 is not within the range of -π/2 to π/2 for inverse sine.
  • What is the value of inverse sine of -√2/2?
    The value is -π/4, since sine of -π/4 equals -√2/2 and -π/4 is within the correct interval.
  • What is the domain for the inverse tangent function?
    The domain for inverse tangent is all real numbers, from negative infinity to infinity.
  • What is the range for the inverse tangent function?
    The range for inverse tangent is all angles between -π/2 and π/2.
  • What is the value of inverse tangent of √3?
    The value is π/3, since tangent of π/3 equals √3 and π/3 is within the correct interval.
  • What is the value of inverse tangent of -1?
    The value is -π/4, since tangent of -π/4 equals -1 and -π/4 is within the correct interval.
  • How do you use a calculator to evaluate an inverse trig function?
    Press the second button and then the corresponding trig function key, enter your value, and ensure you are in radian mode unless otherwise specified.