What is the range of the function y = sin^(-1)(x)?
Correct Answer: [-π/2, π/2]
- Step 1: Understand what y = sin^(-1)(x) means. This is the inverse sine function, also known as 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)) takes a value between -1 and 1 and gives back an angle.
- Step 4: Determine the angles that correspond to the values -1 and 1 in the sine function.
- Step 5: The angle for sin = -1 is -π/2 and for sin = 1 is π/2.
- Step 6: Therefore, the range of the inverse sine function y = sin^(-1)(x) is all angles from -π/2 to π/2.
- Step 7: Write the range in interval notation: [-π/2, π/2].
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