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The range of the function y = sin^(-1)(x) is:
The range of the function y = sin^(-1)(x) is:
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Practice Questions
1 question
Q1
The range of the function y = sin^(-1)(x) is:
(0, π)
[-π/2, π/2]
[-1, 1]
[0, 1]
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The range of y = sin^(-1)(x) is [-π/2, π/2].
Questions & Step-by-step Solutions
1 item
Q
Q: The range of the function y = sin^(-1)(x) is:
Solution:
The range of y = sin^(-1)(x) is [-π/2, π/2].
Steps: 6
Show Steps
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 it is a function (one output for each input).
Step 5: The range of angles for sin^(-1)(x) is from -π/2 to π/2 radians.
Step 6: Therefore, the range of the function y = sin^(-1)(x) is [-π/2, π/2].
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