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The range of sin^(-1)(x) is:

Practice Questions

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

Questions & Step-by-Step Solutions

The range of sin^(-1)(x) is:
  • 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: The angles returned by sin^(-1)(x) are limited to a specific range to ensure that each value corresponds to only one angle.
  • Step 5: The range of angles for sin^(-1)(x) is from -π/2 to π/2 (in radians).
  • Step 6: Therefore, the range of sin^(-1)(x) is written as [-π/2, π/2].
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