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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