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

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

Options:

  1. [-π/2, π/2]
  2. [-1, 1]
  3. [0, π]
  4. [-π, π]

Correct Answer: [-π/2, π/2]

Solution: 

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

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

Practice Questions

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

Questions & Step-by-Step Solutions

What is the range of sin^(-1)(x)?
Correct Answer: [-π/2, π/2]
  • Step 1: Understand what sin^(-1)(x) means. It is the inverse sine function, also called arcsin.
  • 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 of 1 at π/2 and its minimum of -1 at -π/2.
  • Step 5: Therefore, the angles that sin^(-1)(x) can return are between -π/2 and π/2.
  • Step 6: Conclude that the range of sin^(-1)(x) is the set of angles from -π/2 to π/2, which is written as [-π/2, π/2].
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