Question

If sin⁻¹ x = y, then ______.

Options

• 0 ≤ y ≤ π

• `-pi/2 ≤ y ≤ pi/2`

• 0 < y < π

• `-pi/2 < y < pi/2`

Answer 1

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]`