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Question
If sin−1 x = y, then ______.
Options
0 ≤ y ≤ π
`-pi/2 ≤ y ≤ pi/2`
0 < y < π
`-pi/2 < y < pi/2`
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Solution
If sin−1 x = y, then `\underlinebb(-pi/2 ≤ y ≤ pi/2)`.
Explanation:
It is given that sin−1 x = y
We know that the range of the principal value branch of sin−1 is `[-pi/2, pi/2]`.
Then `y ∈ [-pi/2, pi/2]`
Therefore, `[-pi/2 <= y <= pi/2]`
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