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What is the range of the function sin^(-1)(x)?

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Question: What is the range of the function sin^(-1)(x)?

Options:

  1. (-π/2, π/2)
  2. (-1, 1)
  3. (0, π)
  4. (0, 1)

Correct Answer: (-π/2, π/2)

Solution: 

The range of sin^(-1)(x) is (-π/2, π/2).

What is the range of the function sin^(-1)(x)?

Practice Questions

Q1
What is the range of the function sin^(-1)(x)?
  1. (-π/2, π/2)
  2. (-1, 1)
  3. (0, π)
  4. (0, 1)

Questions & Step-by-Step Solutions

What is the range of the function sin^(-1)(x)?
  • Step 1: Understand what sin^(-1)(x) means. It is the inverse sine function, also known as arcsin(x).
  • Step 2: Know that the sine function (sin) takes an angle and gives a value between -1 and 1.
  • Step 3: The inverse sine function (sin^(-1)(x)) takes a value between -1 and 1 and gives back an angle.
  • Step 4: Determine the angles that correspond to the values of sin. The sine function reaches its maximum and minimum at -π/2 and π/2.
  • Step 5: Conclude that the output (range) of sin^(-1)(x) is the set of angles from -π/2 to π/2, not including the endpoints.
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